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 dimensional formula of Planck's constant h is

(a)

[ML²T^-1]

(b)

[ML²T³]

(c)

[MLT^-1]

(d)

[ML³T^-3]

The dimensional formula for gravitational constant G is

(a)

[ML³T^-2]

(b)

[M^-1L³T^-2]

(c)

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

(d)

[ML^-3T²]

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]

The dimension of \({\left( {\mu}_{0}{\epsilon}_{0} \right)}^{{{1}\over{2}}}\) is

(a)

length

(b)

time

(c)

velocity

(d)

force

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)

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

The branch of physics deals with the relation between space, time and energy are _______________.

(a)

astrophysics

(b)

relativity

(c)

acoustics

(d)

atomic physics

Two objects of masses m₁ and m₂ fall from the heights h₁ and h₂ respectively. The ratio of the magnitude of their momenta when they hit the ground is

(a)

\(\sqrt { \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \)

(b)

\(\sqrt { \frac { { { m }_{ 1 }h }_{ 1 } }{ { { m }_{ 2 }h }_{ 2 } } } \)

(c)

\(\frac { { m }_{ 1 } }{ { m }_{ 2 } } \sqrt { \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \)

(d)

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

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)

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.

Relative velocity of A with respect to B when A and B are in the opposite direction is ______________

(a)

\(\vec{V}_{A}-\vec{V}_{B}\)

(b)

\(\vec{V}_{B}-\vec{V}_{A}\)

(c)

\(\vec{V}_{A}+\vec{V}_{B}\)

(d)

\(\sqrt{V_A^2+2V_B^2+2V_AV_Bcos\theta}\)

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

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

Which of the following force tends to stopthe moving object?

(a)

Frictional force

(b)

Magnetic force

(c)

Gravitational force

(d)

Electric force

A uniform force of (2\(\hat { i }\)+\(\hat { j }\)) N acts on a particle of mass 1 kg. The particle displaces from position (3\(\hat { j }\)+\(\hat { k }\)) m to (5\(\hat { i }\)+3\(\hat { j }\)) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

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 1 kg is thrown upwards with a velocity 20 ms^-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?(Take g = 10 ms^-2)

(a)

20 J

(b)

30 J

(c)

40 J

(d)

10 J

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

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 particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = kx + ax³. Here, k and a are positive constants. For x ≥ 0, the functional form of the potential, energy U(x) of the particles

(a)

(b)

(c)

(d)

In perfect inelastic collision, the relative velocity of the bodies _____________.

(a)

before impact is zero

(b)

before impact is equal to that after impact

(c)

after impact is zero

(d)

None of the above is true

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 ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

(a)

5: 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

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)

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

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

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis xx¹ which is touching to two shells and passing through diameter of third shell. M.I of the system consisting of these three spherial shells about xx¹ axis is ________________.

(a)

3mr²

(b)

4mr²

(c)

16/5mr²

(d)

11/5 mr²

In a two particle system, one particle lies at origin another one lies at a distance of X. Then the position of center of mass of these particles of equal mass is ______________.

(a)

\(\frac{m_2 X_2}{m_1+m_2}\)

(b)

\(\frac{X}{2}\)

(c)

\(\frac{mX}{m_1+m_2}\)

(d)

\(\frac{m_1+m_2}{mX}\)

A planet moving along an elliptical orbit is closest to the Sun at distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are linear speeds at these points respectively. Then the ratio \({v_1\over v_2}\) is

(a)

\({r_2\over r_1}\)

(b)

\(({r_2\over r_1})^2\)

(c)

\({r_1\over r_2}\)

(d)

\(({r_1\over r_2})^2\)

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_A, K_B and K_C respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then
 

(a)

K_A > K_B >K_C

(b)

K_B < K_A < K_C

(c)

K_A < K_B < K_C

(d)

K_B > K_A > K_C

A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth the escape speed from the earth is V_e its speed with respect to the satellite________________.

(a)

will be less than V_e

(b)

will be more than V_e

(c)

will be equal to V_e

(d)

will depend on direction of projection

A small sphere of radius 2cm falls from rest in a viscous liquid. Heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

(a)

2²

(b)

2³

(c)

2⁴

(d)

2⁵

Two wires are made of the same material and have the same volume. The area of cross sections of the first and the second wires are A and 2A respectively. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

(a)

2 F

(b)

4 F

(c)

8 F

(d)

16 F

Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is Δl. If Y represents the Young’s modulus, then which of the following graphs is a straight line?

(a)

\(\Delta\)l verses V

(b)

\(\Delta\)l  verses Y

(c)

\(\Delta\)l  verses F

(d)

\(\Delta\)l  verses \(\frac{1}{l}\)

Two drops of equal radius coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?

(a)

2^1/2:1

(b)

1:1

(c)

2^2/3:1

(d)

none of these

The efficiency of a heat engine working between the freezing point and boiling point of water is

(a)

6.25%

(b)

20%

(c)

26.8%

(d)

12.5%

Universal gas constant is _________________.

(a)

C_p/C_v

(b)

C_p - C_v

(c)

C_p + C_v

(d)

C_v/C_p

The ratio \(\gamma =\frac { { C }_{ p } }{ { C }_{ V } } \) for a gas mixture consisting of 8 g of helium and 16 g of oxygen is

(a)

23/15

(b)

15/23

(c)

27/11

(d)

17/27

If s_P and s_V denote the specific heats of nitrogen gas per unit mass at constant pressure and constant volume respectively, then

(a)

s_P - s_V = 28R

(b)

s_P - s_V = R/28

(c)

s_P - s_V = R/14

(d)

s_P - s_V = R

At which of the following temperature would be molecules of gas have twice the average K.E they have at 20°C?

(a)

40°C

(b)

80°C

(c)

586°C

(d)

313°C

In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be

(a)

an ellipse

(b)

a circle

(c)

a parabola

(d)

a straight line

A simple pendulum has a time period T₁. When its point of suspension is moved vertically upwards according as y = k t², where y is vertical distance covered and k = 1 ms⁻², its time period becomes T₂. Then, \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \) is (g = 10 m s⁻²).

(a)

\(\frac{5}{6}\)

(b)

\(\frac{11}{10}\)

(c)

\(\frac{6}{5}\)

(d)

\(\frac{5}{4}\)

An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is

(a)

4\(\frac { Mg }{ k } \)

(b)

\(\frac { Mg }{ k } \)

(c)

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

(d)

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

A pendulum is hung in a very high building oscillates to and fro motion freely like a simple harmonic oscillator. If the acceleration of the bob is 16 ms⁻² at a distance of 4 m from the mean position, then the time period is

(a)

2 s

(b)

1 s

(c)

2\(\pi\)s

(d)

\(\pi\)s

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

(a)

kgms⁻¹

(b)

kgms⁻²

(c)

kgs⁻¹

(d)

kgs

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in thrid harmonic. The ratio of length of 2 pipes is _____________.

(a)

1: 2

(b)

4: 1

(c)

8: 3

(d)

3: 8