Plus One Public Exam March 2019 One Mark Question Paper

Download Tamil Nadu 11th Standard Physics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

Questions:

Multiple Choice Question

100 x 1 = 100

The relation between torque and angular acceleration is _____________.

(a)

\(\overrightarrow{\tau}=\frac{I}{\overrightarrow{\alpha}}\)

(b)

\(\overrightarrow{\alpha}=\frac{\overrightarrow{\tau}}{I}\)

(c)

\(\overrightarrow{\alpha}=I \overrightarrow{\tau}\)

(d)

\(\overrightarrow{\tau}=\frac{\overrightarrow{\alpha}}{I}\)

If the direction of torque is out of the paper then the rotation produced by the torque is ____________.

(a)

clockwise

(b)

anticlockwise

(c)

striaght line

(d)

random direction

Moment of inertia of a uniform solid cylinder about as axis passing perpendicular to the length and passing through the center is _______________.

(a)

MR²

(b)

M\(\left( \frac { { R }^{ 2 } }{ 2 } +\frac { { l }^{ 2 } }{ 12 } \right) \)

(c)

\(\frac { 1 }{ 2 } \)MR²

(d)

M\(\left( \frac { { R }^{ 2 } }{ 4 } +\frac { { l }^{ 2 } }{ 12 } \right) \)

The distance between the centres of carbon and oxygen atoms in the carbon monoxide gas molecule is 1.13 \(\overset{0}{A}\). The centre of mass of the molecule relative to oxygen atom is _______________.

(a)

0.602 \(\overset{0}{A}\)

(b)

0.527 \(\overset{0}{A}\)

(c)

1.13 \(\overset{0}{A}\)

(d)

0.565 \(\overset{0}{A}\)

For square and rectangular objects center of mass lies at _____________.

(a)

the point where the diagonals meet

(b)

at the corners

(c)

on the center surface

(d)

any point

X = -ky² is represented by _______________.

(a)

(b)

(c)

(d)

A person moving horizontally with velocity \(\vec{V_m}\) The relative velocity of rain with respect to the person is ___________.

(a)

V_R + V_m

(b)

\(\sqrt{V_R+V_m}\)

(c)

V_R - V_m

(d)

\(\sqrt{V_R^2+V_m^2}\)

The unit of momentum is ____________.

(a)

kg m s^-1

(b)

kg m² s^-2

(c)

kg m² s^-1

(d)

kg^-1 m² s^-1

The ratio of the displacement vector to the corresponding time interval is ____________.

(a)

average speed

(b)

average velocity

(c)

instantaneous speed

(d)

instantaneous velocity

10.

From this velocity-time graph, which of the following is correct?

(a)

Constant acceleration

(b)

Variable acceleration

(c)

Constant velocity

(d)

Variable acceleration

11.

A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. Which of the following is conserved?

(a)

Momentum and kinetic energy

(b)

kinetic energy alone

(c)

Momentum alone

(d)

potential energy alone

12.

The kinetic energy is not conserved in ______________.

(a)

Elastic collision

(b)

Inelastic collision

(c)

both (a) and (b)

(d)

none

13.

The dimension of power is_________________.

(a)

ML²T^-2

(b)

ML²T^-3

(c)

ML^-2T²

(d)

ML^-2T³

14.

The unit of power is _______________.

(a)

(b)

(c)

Js^-1

(d)

both (b) and (c)

15.

The period of a simple pendulum is recorded as 2.56s, 2.42s, 2.71s, and 2.80s respectively. The average absolute error is___________________

(a)

0.1_S

(b)

0.2_S

(c)

1.0_S

(d)

0.11_S

16.

Two blocks of masses m₁ and m₂ (m₁ > m₂) in contact with each other on frictionless, horizontal surface. If a horizontal force F is given on m₁, set into motion with acceleration a, then reaction force on mass m₁ by m₂ is ____________.

(a)

\(\frac { { Fm }_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } \)

(b)

\(\frac { { m }_{ 1 }{ m }_{ 2 } }{ { Fm }_{ 1 } } \)

(c)

\(\frac { { m }_{ 1 }{ m }_{ 2 } }{ { Fm }_{ 2 } } \)

(d)

\(\frac { { Fm }_{ 2 } }{ { m }_{ 1 }+m_{ 2 } } \)

17.

The comparison of any physical quantity with its standard unit is known as__________

(a)

fundamental quantities

(b)

measurement

(c)

dualism

(d)

derived quantities

18.

To get the best possible true value of the quantity___________has to be taken.

(a)

rms value

(b)

net value

(c)

arithmetic mean

(d)

mode

19.

One light year is________________.

(a)

3.153\(\times\)10⁷ m

(b)

1.496\(\times\)10⁷ m

(c)

9.46\(\times\)10¹² km

(d)

3.26\(\times\)10¹⁵ m

20.

A ratio signal sent towards the distant planet, returns after "t"s. If "c" is the speed of radio waves then the distance of the planet and from the earth is______________.

(a)

\(c\frac{t}{2}\)

(b)

ct²

(c)

2ct

(d)

\(c^2\frac{t^2}{2}\)

21.

When a force is applied on a body, it can change ____________.

(a)

velocity

(b)

momentum

(c)

direction of motion

(d)

all the above

22.

Two masses of 1 g and 9 g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is _______________.

(a)

1: 9

(b)

9: 1

(c)

1: 3

(d)

3:1

23.

Two equal masses m₁ and m₂ moving along the same straight line with velocities +3 m/s and -5 m/s respectively collide elastically. Their velocities after the collision will be respectively _______________.

(a)

- 4 m/s and +4 m/s

(b)

+4 m/s for both

(c)

- 3 m/s and +5 m/s

(d)

- 5 m/s and + 3 m/s

24.

A vertical spring with force constant k is fixed on a table. A.ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is _____________.

(a)

\(mg(h+d)-\frac{1}{2}kd^2\)

(b)

\(mg(h-d)-\frac{1}{2}kd^2\)

(c)

\(mg(h-d)+\frac{1}{2}kd^2\)

(d)

\(mg(h+d)+\frac{1}{2}kd^2\)

25.

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is _____________.

(a)

40ms^-1

(b)

120ms^-1

(c)

100ms^-1

(d)

80ms^-1

26.

A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?

(a)

(b)

(c)

(d)

27.

Two identical balls A and B having velocities of 0.5 ms^-1 and -0.3 ms^-1 respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be ______________.

(a)

-0.5 ms^-1 and 0.3 ms^-1

(b)

0.5 ms^-1 and -0.3 ms^-1

(c)

-0.3 ms^-1 and 0.5 ms^-1

(d)

0.3 ms^-1 and 0.5 ms^-1

28.

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom?

(a)

\(\sqrt { 2gh } \)

(b)

\(\sqrt { \frac { 3 }{ 4 } gh } \)

(c)

\(\sqrt { \frac { 4 }{ 3 } gh } \).

(d)

\(\sqrt { 4gh } \)

29.

A symmetrical lamina of mass M consists of a square shape with equilateral triangular section over each of the side of the square as shown. The MI of the lamina about an axis through its centre of mass and perpendicular to its plane is 2.4 Ma², The moment of inertia of the lamina about AB, at one of the vertices parallel to the line Joining the corners passing through O; is _______________.

(a)

8.67 Ma²

(b)

6.4 Ma²

(c)

4.2 Ma²

(d)

2.4 Ma²

30.

Motion of a particle is given by equation s = (3t³+7t²+14t+8)m. The value of acceleration of the particle at t=1 sec is _____________.

(a)

10m/s²

(b)

32m/s²

(c)

23m/s²

(d)

16m/s²

31.

A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 m/s². What would be the reading on the scale? (g = 10 m/s²).

(a)

zero

(b)

400 N

(c)

800 N

(d)

1200 N

32.

The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is _______________.

(a)

4 ms^-2 upwards

(b)

4 ms^-2 downwards

(c)

14 ms^-2 upwards

(d)

30 ms^-2 downwards

33.

If the heart pumps blood at the rate of M kg per unit time, with constant velocity 'v' the force required is ________________

(a)

\(\frac { M }{ v } \)

(b)

Mv²

(c)

M²v

(d)

34.

A particle if confined to rotate in a circular path with decreasing linear speed. The which of the following is correct?

(a)

\(\bar{L}\) (angular momentum) is conserved about the centre

(b)

only direction of angular momentum \(\bar{L}\) is conserved

(c)

it spiral towards the centre

(d)

its acceleration is towards the centre

35.

Identify the vector quantity among the following _______________.

(a)

distance

(b)

angular momentum

(c)

heat

(d)

energy

36.

The 10, cation of the centre of mass of a sphere is at ______________.

(a)

its top

(b)

its bottom

(c)

geometric centre

(d)

all the above

37.

Head on collision signifies collision with:

(a)

velocities of equal magnitudes

(b)

velocities of different magnitudes

(c)

velocities acting along same straight line out in opposite direction

(d)

velocities acting at right angles

38.

Two springs have their force constant as K₁ and K₂ (k₁ > k₂). When they are stretched by the same force?

(a)

no work is done in case of both the springs

(b)

equal work is done in case of both the springs

(c)

more work is done in case of second spring

(d)

more work is done in case of first spring

39.

The energy possessed by a body by its state of strain is called as____________.

(a)

kinetic energy

(b)

mechanical energy

(c)

potential energy

(d)

none

40.

The same error repeated every time in the series of observation is known as _____________error.

(a)

random

(b)

constant

(c)

gross

(d)

systematic

41.

Which of the following digits are significant?

(a)

zero digits

(b)

zeros at the end without a decimal point

(c)

all zeros between two non-zeros digits, irrespective of the decimal point

(d)

all the above

42.

When a body is stationary ____________.

(a)

there is no force acting on it

(b)

the force acting on it is not in contact with it

(c)

the combination of forces acting on it balances each other

(d)

the body is in vacuum

43.

1 radian = ________.

(a)

50729°

(b)

572.9°

(c)

\(\frac{\pi}{180}\)

(d)

57.295°

44.

A book lying on the table continues in its state of rest unless an external force acts on it. It is due to _____________.

(a)

inertia of rest

(b)

inertia of motion

(c)

inertia of direction

(d)

both (b) and (c)

45.

Second law of Newton gives the ______ definition of force.

(a)

fundamental

(b)

quantitative

(c)

dimensional

(d)

both (b) and (c)

46.

The density of a liquid in CGS system is 0.625 g/cm³. What is its magnitude in SI system?

(a)

625 kg/m³

(b)

0.0625 kg/m³

(c)

0.625 kg/m³

(d)

O.00625 kg/m³

47.

The velocity of a particle at an instant t is 10 m/s. After 5 s the velocity is 20 m/s. The velocity, 3 seconds earlier was ______________

(a)

2 m/s

(b)

3 m/s

(c)

4 m/s

(d)

5 m/s

48.

A shell, in flight explodes into four unequal parts. Which is conserved?

(a)

potential energy

(b)

momentum

(c)

kinetic energy

(d)

both a and c

49.

If a person standing on a rotating disc stretches out his hands the angular speed will ____________.

(a)

Increase

(b)

Decrease

(c)

Remain same

(d)

None

50.

A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. A force F is applied at the free end of the rope. The force exerted by the rope on the block ____________.

(a)

\(\frac { MF }{ M+m } \)

(b)

\(\frac { M+m }{ MF } \)

(c)

\(\frac { M }{ M-m } \) .F

(d)

\(\frac { M-m }{ M } \) .F

51.

A round object of mass M and radius R rolls down without slipping along an inclined plane. The frictional force,

(a)

dissipates kinetic energy as heat

(b)

decreases the rotational motion

(c)

decreases the rotational and transnational motion

(d)

converts transnational energy into rotational energy

52.

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(a)

a line perpendicular to the plane of rotation

(b)

the line making an angle of 45^o to the plane of rotation

(c)

the radius

(d)

tangent to the path

53.

Two discs of same moment of inertia rotating about their regular axes passing through center and perpendicular to the plane of the disc with angular velocities ω₁ and ω₁. They are brought in to contact face to face coinciding with the axis of rotation. The expression for loss of energy during this process is

(a)

\(\frac{1}{4}\)\(I(\omega _{1}-\omega _{2})^2\)

(b)

\(I(\omega _{ 1 }-\omega _{ 2 })^{ 2 }\)

(c)

\(\frac{1}{8}\)\(I(\omega _{1}-\omega _{2})^2\)

(d)

\(\frac{1}{2}I\)\((\omega _{1}-\omega _{2})^2\)

54.

The speed of the center of a wheel rolling on a horizontal surface is v_o. A point on the rim in level with the center will be moving at a speed of,

(a)

zero

(b)

v_o

(c)

\(\sqrt{2}\)v_o

(d)

2v_o

55.

The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is,

(a)

\( \sqrt \frac{4}{3}gh\)

(b)

\( \sqrt \frac{10}{7}gh\)

(c)

\(\sqrt{2gh}\)

(d)

\( \sqrt \frac{1}{2}gh\)

56.

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

(a)

15MR²/32

(b)

13MR²/32

(c)

11MR²/32

(d)

9MR²/32

57.

A disc of the moment of inertia I_a is rotating in a horizontal plane about its symmetry axis with a constant angular speed \(\omega\). Another disc initially at rest of moment of inertia I_b is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

\(\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(b)

\(\frac { { I }_{ b }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(c)

\(\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(d)

\(\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

58.

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(a)

\(\frac{2}{3}\)k

(b)

\(\frac{3}{2}\)k

(c)

(d)

59.

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U(x) versus x will be (where U, is the potential , energy function)

(a)

(b)

(c)

(d)

60.

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(a)

(b)

v²

(c)

v³

(d)

v⁴

61.

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

62.

The potential energy of a system increases, if work is done

(a)

by the system against a conservative force

(b)

by the system against a non-conservative force

(c)

upon the system by a conservative force

(d)

upon the system by a non- conservative force

63.

A particle undergoes uniform circular motion. The angular momentum of the particle remain conserved about,

(a)

the center point of the circle

(b)

the point on the circumference of the circle

(c)

any point inside the circle

(d)

any point outside the circle

64.

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a)

(b)

L/2

(c)

(d)

L/\(\sqrt{2}\)

65.

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

(a)

increases

(b)

decreases

(c)

remains constant

(d)

depends on direction of rotation

66.

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

(a)

0.25 rad s^-2

(b)

25 rad s^-2

(c)

5 ms^-2

(d)

25 ms^-2

67.

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

(a)

zero

(b)

increasing with x

(c)

decreasing with x

(d)

remaining constant

68.

A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

(a)

mv²

(b)

\(\frac{3}{2}\)mv²

(c)

2mv²

(d)

4mv²

69.

A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

(a)

\(\sqrt2:1\)

(b)

\(1:\sqrt2\)

(c)

2:1

(d)

1:2

70.

A couple produces,

(a)

pure rotation

(b)

pure translation

(c)

rotation and translation

(d)

no motion

71.

The center of mass of a system of particles does not depend upon,

(a)

position of particles

(b)

relative distance between particles

(c)

masses of particles

(d)

force acting on particle

72.

The fractional error \(\left( {{\triangle x}\over{x}} \right)\) _____________.

(a)

\(\pm\left( {{\triangle x}\over{x}} \right)\)

(b)

\(\pm n\left( {{\triangle a}\over{a}}\right)\)

(c)

\(\pm n \log_e \left( {{\triangle a}\over{a}}\right)\)

(d)

\(\pm n \log_{10}{{\triangle a}\over{a}}\)

73.

Which of the following Statement is true?

(a)

Velocity is a fundamental unit

(b)

Solar day = 24 hours.

(c)

1 Shake = 10⁴s

(d)

mass is a derived unit

74.

If a person moving from pole to equator, the centrifugal force acting on him

(a)

increases

(b)

decreases

(c)

remains the same

(d)

increases and then decreases

75.

The centrifugal force appears to exist

(a)

only in inertial frames

(b)

only in rotating frames

(c)

in any accelerated frame

(d)

both in inertial and non-inertial frames

76.

When the object is moving at constant velocity on the rough surface

(a)

net force on the object is zero

(b)

no force acts on the object

(c)

only external force acts on the object

(d)

only kinetic friction acts on the object

77.

Force acting on the particle moving with constant speed is

(a)

always zero

(b)

need not be zero

(c)

always non zero

(d)

cannot be concluded

78.

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F₁ is applied from the left. Later only a force F₂ is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F₁ :F₂ is

(a)

1:1

(b)

1:2

(c)

2:1

(d)

1:3

79.

Choose appropriate free body diagram for the particle experiencing net acceleration along negative y direction. (Each arrow mark represents the force acting on the system).

(a)

(b)

(c)

(d)

80.

Two masses m₁ and m₂ are experiencing the same force where m₁ < m₂.The ratio of their acceleration \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \) is _____________.

(a)

(b)

less than 1

(c)

greater than 1

(d)

all the three cases

81.

A vehicle is moving along the positive x direction, if sudden brake is applied, then

(a)

frictional force acting on the vehicle is along negative x direction

(b)

frictional force acting on the vehicle is along positive x direction

(c)

no frictional force acts on the vehicle

(d)

frictional force acts in downward direction

82.

An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure.The minimum value of the force F is

(a)

Less than mg

(b)

Equal to mg

(c)

Greater than mg

(d)

Cannot determine

83.

When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to

(a)

inertia of direction

(b)

inertia of motion

(c)

inertia of rest

(d)

absence of inertia

84.

If an object is thrown vertically up with the initial speed u from the ground, then the time taken by the object to return back to ground is

(a)

\(\frac{u^2}{2g}\)

(b)

\(\frac{u^2}{g}\)

(c)

\(\frac{u}{2g}\)

(d)

\(\frac{2u}{g}\)

85.

If a particle executes uniform circular motion, choose the correct statement

(a)

The velocity and speed are constant

(b)

The acceleration and speed are constant.

(c)

The velocity and acceleration are constant.

(d)

The speed and magnitude of acceleration are constant.

86.

A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

(a)

(b)

(c)

(d)

87.

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

(a)

(b)

(c)

(d)

88.

If the velocity is \(\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k } \), then the magnitude of acceleration at t = 0.5s is

(a)

1 ms^-2

(b)

2 ms^-2

(c)

zero

(d)

-1 ms^-2

89.

If a particle has negative velocity and negative acceleration, its speed

(a)

increases

(b)

decreases

(c)

remains same

(d)

zero

90.

Which one of the following physical quantities cannot be represented by a scalar?

(a)

Mass

(b)

length

(c)

momentum

(d)

magnitude of acceleration

91.

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

(a)

\({{\sqrt{hG}}\over{{c}^{{{3}\over{2}}}}}\)

(b)

\({{\sqrt{hG}}\over{{c}^{{{5}\over{2}}}}}\)

(c)

\(\sqrt{{{hc}\over{G}}}\)

(d)

\(\sqrt{{{Gc}\over{{h}^{{{3}\over{2}}}}}}\)

92.

If the force is proportional to square of velocity, then the dimension of proportionality constant is

(a)

[MLT⁰]

(b)

[MLT^-1]

(c)

[MLT^-2T]

(d)

[MLT^-1T⁰]

93.

The density of a material in CGS system of units is 4 g cm^-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

(a)

0.04

(b)

0.4

(c)

(d)

400

94.

The dimensional formula for gravitational constant G is

(a)

[ML³T^-2]

(b)

[M^-1L³T^-2]

(c)

[M^-1L^-3T^-2]

(d)

[ML^-3T²]

95.

The velocity of a particle v at an instant t is given by v = at + br². The dimensions of b is

(a)

[L]

(b)

[LT^-1]

(c)

[LT^-2]

(d)

[LT^-3]

96.

The dimensional formula of Planck's constant h is

(a)

[ML²T^-1]

(b)

[ML²T³]

(c)

[MLT^-1]

(d)

[ML³T^-3]

97.

Which of the following has the highest number of significant figures?

(a)

0.007 m²

(b)

2.64\(\times\)10²⁴kg

(c)

0.0006032 m²

(d)

6.3200 J

98.

The length of a body is measured as 3.51 m, if the accuracy is 0.01 mm, then the percentage error in the measurement is

(a)

35.1%

(b)

(c)

0.28%

(d)

0.035%

99.

If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

(a)

(b)

(c)

(d)

100.

One of the combinations from the fundamental physical constants is \({{hc}\over{G}},\) The unit of this expression is

(a)

Kg²

(b)

m³

(c)

S^-1

(d)

Visit QB365-SLMS - https://www.qb365.in/slms/

Answers Key:

Multiple Choice Question

100 x 1 = 100

(b)
\(\overrightarrow{\alpha}=\frac{\overrightarrow{\tau}}{I}\)

(a)
clockwise

(d)
M\(\left( \frac { { R }^{ 2 } }{ 4 } +\frac { { l }^{ 2 } }{ 12 } \right) \)

(b)
0.527 \(\overset{0}{A}\)

(a)
the point where the diagonals meet

(d)
\(\sqrt{V_R^2+V_m^2}\)

(b)
kg m² s^-2

(b)
average velocity

10.

(b)
Variable acceleration

11.

(d)
potential energy alone

12.

(b)
Inelastic collision

13.

(b)
ML²T^-3

14.

(d)
both (b) and (c)

15.

(d)
0.11_S

16.

(a)
\(\frac { { Fm }_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } \)

17.

(b)
measurement

18.

19.

20.

21.

(a)
velocity

22.

23.

(d)
- 5 m/s and + 3 m/s

24.

(a)
\(mg(h+d)-\frac{1}{2}kd^2\)

25.

26.

27.

(b)
0.5 ms^-1 and -0.3 ms^-1

28.

29.

(a)
8.67 Ma²

30.

(b)
32m/s²

31.

(d)
1200 N

32.

(a)
4 ms^-2 upwards

33.

(d)
Mv

34.

(b)
only direction of angular momentum \(\bar{L}\) is conserved

35.

(b)
angular momentum

36.

37.

38.

39.

(a)
kinetic energy

40.

(b)
constant

41.

42.

43.

(d)
57.295°

44.

(a)
inertia of rest

45.

(d)
both (b) and (c)

46.

(a)
625 kg/m³

47.

48.

(b)
momentum

49.

(b)
Decrease

50.

(a)
\(\frac { MF }{ M+m } \)

51.

(d)
converts transnational energy into rotational energy

52.

(a)
a line perpendicular to the plane of rotation

53.

Moment of inertia of a disc passing through
\(\text { centre } I=\frac{1}{2} M R^{2}\)
\(\text { Energy of the first disc }=\frac{1}{4} I \omega_{1}^{2}\)
\(\text { Energy of the second disc }=\frac{1}{4} I \omega_{2}^{2}\)
\(\text { Loss of energy }=\frac{1}{4} I\left(\omega_{1}-\omega_{2}\right)^{2}\)

54.

\(v_{0}=r \omega ; \quad \therefore v_{0} \alpha r\)
For a wheel (uniform ring) the distance of a point on the rim in level with the center
\(\text { [i.e., radius] is } \sqrt{2} r\)
\(\therefore \text { The speed of the center is } \sqrt{2} v_{0}\)

55.

Potential energy = Translational kinetic energy + Rotational kinetic energy
\(m g h=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2} \)
\(=\frac{1}{2} m v^{2}+\frac{1}{2} \times \frac{2}{5} M R^{2} \times \frac{v^{2}}{R^{2}}\left[\omega=\frac{v}{R}\right] \)
\(=\frac{1}{2} m v^{2}+\frac{1}{5} m v^{2} \)
\(=\frac{5 m v^{2}+2 m v^{2}}{10}=\frac{7 m v^{2}}{10} \)
\(m g h=\frac{7 m v^{2}}{10} \)
\(g h=\frac{7 v^{2}}{10} \)
\(\therefore v^{2}=\frac{10 g h}{7} \)
\(\therefore v=\frac{\sqrt{10 g h}}{7} \)

56.

Moment of inertia of a disc
\(\mathrm{I}_{1}=\frac{M R^{2}}{2}\)
\(\text { Mass of small disc }=\frac{M}{\pi R^{2}} \times \pi \times\left(\frac{R}{2}\right)^{2}\)
\(=\frac{M}{\pi R^{2}} \times \frac{\pi R^{2}}{4}=\frac{M}{4}\)
By the theorem of parallel axis, the moment of inertia of the small disc. About an axis passing through 0 is
\(I_{2} =\frac{1}{2} \times \frac{M}{4}\left(\frac{R}{2}\right)^{2}+\frac{M}{4}\left(\frac{R}{2}\right)^{2} \)
\(=\frac{M}{8} \times \frac{R^{2}}{4}+\frac{M}{4} \times \frac{R^{2}}{4} \)
\(=\frac{M R^{2}}{32}+\frac{M R^{2}}{16}=\frac{M R^{2}+2 M R^{2}}{32} \)
\(I_{2} =\frac{3 M R^{2}}{32} \)
Moment of inertia of the remaining part is I= I₁ - I₂
\(=\frac{M R^{2}}{2}-\frac{3 M R^{2}}{32} \)
\(=\frac{16 M R^{2}-3 M R^{2}}{32}=\frac{13 M R^{2}}{32}\)
\(I =\frac{13 M R^{2}}{32} \)

57.

The moments of inertia of two discs are I_a and I_b respectively The angular velocity of the disc A is \(\omega\).
The sum of kinetic energies of two discs before coming in contact is \(k_{1}=\frac{1}{2} I_{a} \omega_{1}^{2}+\frac{1}{2} I_{b} \omega_{2}^{2}\)
\(\text { But angular velocity of the disc be is } \omega_{2}=0 \ \text {(rest)}\)
\(\therefore k_{1}=\frac{1}{2} I_{a} \omega_{1}^{2}\)
The final kinetic energy of the two discs system \(k_{2}=\frac{1}{2} \frac{I_{a}^{2} \omega_{1}^{2}}{I_{a}+I_{b}}\)
The loss of kinetic energy is
\(k_{1}-k_{2} =\frac{1}{2} I_{a} \omega^{2}-\frac{1}{2}\left[\frac{I a^{2} \omega_{1}^{2}}{I_{a}+I_{2 b}}\right] \)
\(=\frac{1}{2} \frac{\left[I_{1}\left(I_{a}+I_{b}\right) \omega^{2}-I_{a}^{2} \omega^{2}\right]}{I_{a}+I_{b}} \)
\(k_{1}-k_{2} =\frac{1}{2} \frac{I_{a} b}{\left(I_{a}+I_{b}\right)} \omega^{2} \)

58.

For any spring kl = constant
Length of the longer piece
\(=\frac{2 l}{3} \)
\(\therefore k^{1} \times \frac{2 l}{3} =k l \)
\(\therefore k^{1}=\frac{k l \times 3}{2 l}=\frac{3}{2} k \)
\(\therefore k^{1}=\frac{3}{2} k \)

59.

For a conservative force
\(F=-\frac{d v}{d t} \)
\(\int_{0}^{u(x)} d v=-\int_{0}^{x} F d x=-\int_{0}^{x} k x d x \)
\(\text { As } v(0)=0\)
\(U(x)=-\frac{k x^{2}}{2}\)
Thus, the graph of U(x) versus (x) will be a parabola, symmetric about U - ax is bying below x - ax is with its vertex at the origin. Hence the correct answer is C

60.

\(\text { Force }=v \frac{d m}{d t}\)
\(=v \frac{d}{d t} \text { (volume } \times \text { density) }\)
\(=v \frac{d}{d t}(A x p) \)
\(=v A p \frac{d x}{d t} \)
\(=v \times A p \times v \)
\(=A p v^{2} \)
Power = Force x Velocity
\(=A p v^{2} \times v=A p v^{3}\)
\(\therefore \text { Power } \alpha v^{3}\)

61.

\(\text { Kinetic energy } E_{k}=\frac{p^{2}}{2 m}\)
\(\frac{\Delta E_{k}}{E_{k}}=\frac{2 \Delta p}{p}\)
\(\text {Given that } \frac{\Delta p}{p}=0.1\)
∴ Increase in kinetic energy
\(\frac{\Delta E_{k}}{E_{k}}=2 \frac{\Delta p}{p} \)
\(\frac{\Delta E_{k}}{E_{k}}=2 \times 0.1=0.2 \% \)

62.

(a)
by the system against a conservative force

63.

(a)
the center point of the circle

64.

\(K \cdot E=\frac{1}{2} I \omega^{2} ; \quad L=I \omega ; \quad K \cdot E=\frac{2^{2}}{2^{2}} \)
\(\therefore K \cdot E \alpha L^{2} \quad E_{1} \alpha L_{1}^{2} \quad E_{2} \alpha L_{2}^{2}\)
\(\frac{E_{1}}{E_{2}}=\left(\frac{L_{1}}{L_{2}}\right)^{2} \)
\(\text { Here } E_{1}=E \quad E_{2}=\frac{E}{2} \)
\(L_{1}=L \quad \quad L_{2}=? \)
\(\frac{E}{\frac{E}{2}}=\left(\frac{L}{L_{2}}\right)^{2} \)
\(\frac{2 E}{E}=\left(\frac{L}{L_{2}}\right)^{2}\left(\frac{L_{1}}{L_{2}}\right)^{2}=2 \)
\(\therefore \frac{L}{L_{2}}=\sqrt{2} \)
\(L_{2}=\frac{L}{\sqrt{2}} \)

65.

(a)
increases

66.

\(m=3 \mathrm{~kg} \quad r=40 \times 10^{-2} \mathrm{~m}=0.4 \mathrm{~m}\)
\(\text { Force }=30 N\)
Moment of inertia of a hollow-cylinder I= MR²
\(=3 \times\left(40 \times 10^{-2}\right)^{2} \)
\(=3 \times 0.4 \times 0.4=0.48 \mathrm{kgm}^{2} \)
\( F R =I \alpha \)
\(30 \times 40 \times 10^{-2}=0.48 d \)
\(d=\frac{12}{0.48}=\frac{1200}{48}=25 \mathrm{rad} \mathrm{s}^{-2} \)
\(\alpha=25 \mathrm{rad} \mathrm{s}^{-2} \)

67.

(d)
remaining constant

68.

Using law of conservation of momentum,
\(2 m v =\sqrt{m^{2} v^{2}+m^{2} v^{2}} \)
\(=\sqrt{2 m^{2} v^{2}} \)
\(v =\frac{\sqrt{2} m v}{2 m}=\frac{v}{\sqrt{2}} \)
Energy released in explosion = \(2 \times \frac{1}{2} m v^{2} +\frac{1}{2} \times 2 m \times\left(\frac{v^{2}}{\sqrt{2}}\right)^{2} \)
\(=m v^{2}+m \times \frac{v^{2}}{2} \)
\(=\frac{3}{2} m v^{2} \)

69.

\(m_{1} =1, \quad m_{2}=2 \)
\(K . E . =m g(h-x) \)
\(\text { For both balls }(h-x)\)
\(=40 \text { i.e.) Same }\)
\(g=\text { constant }\)
\(\therefore K \cdot E_{1}=m_{1} g(h-x)=m_{1} g \times 40 \)
\(K \cdot E_{2}=m_{2} g(h-x)=m_{2} g \times 40 \)
\(\therefore \frac{K \cdot E_{1}}{K \cdot E_{2}}=\frac{m_{1} g \times 40}{m_{2} g \times 40}=\frac{m_{1}}{m_{2}} \)
\( \therefore K \cdot E_{1}: K \cdot E_{2}=1: 2 \)

70.

(a)
pure rotation

71.

(d)
force acting on particle

72.

(b)
\(\pm n\left( {{\triangle a}\over{a}}\right)\)

73.

(b)
Solar day = 24 hours.

74.

(a)
increases

75.

(b)
only in rotating frames

76.

(a)
net force on the object is zero

77.

(b)
need not be zero

78.

79.

80.

81.

(a)
frictional force acting on the vehicle is along negative x direction

82.

83.

(a)
inertia of direction

84.

\(\text {Time of flight }=\frac{2 u}{g}\)

85.

It is a uniform circular motion. So the direction of velocity changes but not the magnitude. Therefore speed in considered constant. Again magnitude of acceleration does not change.

86.

Distance travelled \(s=\frac{1}{2} g t^{2} ; s \alpha t^{2}\). The ratio of distances travelled by a freely falling body will be with ratio 1:4:9:...

87.

Initially velocity has maximum value and at maximum height velocity becomes zero. After that the velocity becomes negative

88.

\(\vec{v}=2 \hat{l}+t^{2} \hat{j}-9 \vec{k}\)
\(\vec{a}=\frac{d \vec{v}}{d t}=2 t \hat{j}\)
\(\text { When } t=0.5 \mathrm{~s}\)
\(a=1 \mathrm{~ms}^{-2}\)

89.

Velocity and acceleration are in the same direction: So speed increases.

90.

Mass, length are scalars. Acceleration is a vector but magnitude of acceleration is a scalar

91.

Dimension of Planck's constant is \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]\)
Dimension of Gravitational constant is \(\left[\mathrm{M}^{-1} \mathrm{~L}^{+3} \mathrm{~T}^{-1}\right]\)
Dimension of Velocity constant is LT^-1
Dimension of Length is L
\(\therefore \text { Dimension of } \frac{\sqrt{h G}}{C^{\frac{3}{2}}}\)
\(=\frac{\sqrt{\left(\mathrm{ML}^{2} \mathrm{~T}^{-1}\right)\left(\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right)}}{\left(\mathrm{LT}^{-1}\right)^{3 / 2}} \)
\(=\frac{\sqrt{\mathrm{L}^{5} \mathrm{~T}^{-3}}}{\mathrm{~L}^{3 / 2} \mathrm{~T}^{-3 / 2}} \)
\(=\frac{\mathrm{L}^{5 / 2} \mathrm{~T}^{-3 / 2}}{\mathrm{~L}^{3 / 2} \mathrm{~T}^{-3 / 2}} \)
\(=\mathrm{L}^{5 / 2-3 / 2} \mathrm{~T}^{3 / 2+3 / 2}=\mathrm{L}^{1} \mathrm{~T}^{0}=\mathrm{L}\)
Dimension of length = L

92.

F = kv²
Dimensional of k
\(=\frac{\text { Dimension of } \mathrm{F}}{\text { Dimension of }(v)^{2}}\)
\(=\frac{\mathrm{MLT}^{-2}}{\left(\mathrm{LT}^{-1}\right)^{2}}=\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}^{2} \mathrm{~T}^{-2}} \)
\(=\left[\mathrm{ML}^{-1-2} \mathrm{~T}^{-2+2}\right] \)
Dimension of proportionality constant \(=\left[\mathrm{ML}^{-1} \mathrm{~T}^{0}\right]\)

93.

94.

\(\text { Gravitational constant } G=\frac{F r^{2}}{m_{l} m_{2}}\)
\(\text { Dimensional formula of } \mathrm{G}=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^{2}\right]}{[\mathrm{M}][\mathrm{M}]}\)
\(=\frac{\mathrm{ML}^{3} \mathrm{~T}^{-2}}{\mathrm{M}^{2}}=\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\)

95.

\(v=a t+b t^{2}\)
\(\text { Dimensional equation is } \mathrm{LT}^{-1}\)
\(=a T=b T^{2}\)
\(\therefore \text { The dimension of } b=\frac{\mathrm{LT}^{-1}}{\mathrm{~T}^{2}}=\mathrm{LT}^{-3}\)

96.

Dimensional formula of Planck's
\(\text { constant }=\frac{\text { Energy }}{\text { Frequency }}=\frac{\mathrm{ML}^{2} \mathrm{~T}^{-2}}{\mathrm{~T}^{-1}}\)
\(=M L^{2} T^{-2+1}=M L^{2} T^{-1}\)

97.

The number of significant figures of 6.3200 J is 5

98.

\(\Delta l =0.01 \)
\(l =3.51 \)
\(\% \text { error } =\frac{\Delta l}{l} \times 100=\frac{0.01}{3.51} \times 100 \)
\(=0.00284 \times 100 \)
\(=0.284=0.28 \% \)

99.

\(T =2 \pi \sqrt{\frac{l}{g}} \)
\(g =4 \pi^{2} l / T^{2} \)
\(\frac{d g}{g} =\frac{d l}{l}-\frac{2 d T}{T} \)
\(\frac{d g}{g} \% =\left(\frac{d l}{l}\right) \%-2\left(\frac{d T}{T}\right) \% \)
\(=1 \%-2 \times(-3 \%) \)
\(=1+6=7 \% \)

100.

Unit of a (Planck's constant) - Js
Unit of c (Velocity of light) - ms^-1
Unit of G (Gravitational Constant) - \(\frac{\mathrm{Nm}^{2}}{\mathrm{Kg}^{2}}\)
\(\therefore \text { Unit of } \frac{h c}{G} \text { is }=\frac{J s \times m s^{-1}}{N m^{2} / k g^{2}} \)
\(=\frac{N m s \times m s^{-1} \times k g^{2}}{N m^{2}}[J=N m] =\mathrm{kg}^{2}\)