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)

m

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)

4%

(b)

5%

(c)

6%

(d)

7%

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)

1%

(c)

0.28%

(d)

0.035%

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

The dimensional formula of Planck's constant h is

(a)

[ML²T^-1]

(b)

[ML²T³]

(c)

[MLT^-1]

(d)

[ML³T^-3]

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]

The dimensional formula for gravitational constant G is

(a)

[ML³T^-2]

(b)

[M^-1L³T^-2]

(c)

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

(d)

[ML^-3T²]

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)

40

(d)

400

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]

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)

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

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

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)

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

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

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

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

(a)

random

(b)

constant

(c)

gross

(d)

systematic

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)

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

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

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

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

(a)

fundamental quantities

(b)

measurement

(c)

dualism

(d)

derived quantities

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

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

(a)

Mass

(b)

length

(c)

momentum

(d)

magnitude of acceleration

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

(a)

increases

(b)

decreases

(c)

remains same

(d)

zero

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

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)

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)

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.

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)

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

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

1 radian = ________.

(a)

50729°

(b)

572.9°

(c)

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

(d)

57.295°

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

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

(a)

Constant acceleration

(b)

Variable acceleration

(c)

Constant velocity

(d)

Variable acceleration

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

(a)

average speed

(b)

average velocity

(c)

instantaneous speed

(d)

instantaneous velocity

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

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)

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

X = -ky² is represented by _______________.

(a)

(b)

(c)

(d)

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

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

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

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

(a)

1

(b)

less than 1

(c)

greater than 1

(d)

all the three cases

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)

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

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

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

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

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

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

Second law of Newton gives the ______ definition of force.

(a)

fundamental

(b)

quantitative

(c)

dimensional

(d)

both (b) and (c)

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)

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

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)

Mv

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

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

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

(a)

velocity

(b)

momentum

(c)

direction of motion

(d)

all the above

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)

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

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

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

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

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

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 %

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)

v

(b)

v²

(c)

v³

(d)

v⁴

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)

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)

3k

(d)

6k

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

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

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

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

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

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)

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

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)

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

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

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

The unit of power is _______________.

(a)

J

(b)

W

(c)

Js^-1

(d)

both (b) and (c)

The dimension of power is_________________.

(a)

ML²T^-2

(b)

ML²T^-3

(c)

ML^-2T²

(d)

ML^-2T³

The kinetic energy is not conserved in ______________.

(a)

Elastic collision

(b)

Inelastic collision

(c)

both (a) and (b)

(d)

none

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

A couple produces,

(a)

pure rotation

(b)

pure translation

(c)

rotation and translation

(d)

no motion

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

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

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

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

(a)

L

(b)

L/2

(c)

2L

(d)

L/\(\sqrt{2}\)

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

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)

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

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

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)

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

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

Two discs of same moment of inertia rotating about their regular axis 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)

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

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

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

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

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

Identify the vector quantity among the following _______________.

(a)

distance

(b)

angular momentum

(c)

heat

(d)

energy

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

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

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)

\(\sqrt { 4gh } \)

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

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 \(\overset{0}{A}\)

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

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

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)

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