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%

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 pairs of quantities and their units is a proper match?

(a)

Electric charge - C

(b)

Pressure - Pa

(c)

Power - JS^-1

(d)

Moment of inertia - Kg m^-2

The dimension of a quantity \(hy \over c\) where h is the planck's constants, \(\gamma\) is the frequency and c is the velocity of light are _______________.

(a)

MT^-1

(b)

MLT^-1

(c)

MLT^-2

(d)

ML²T²

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)

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

If \(\vec A\) and \(\vec B\) are the sides of triangle, then area of triangle ____________.

(a)

\(\frac{1}{2}|\vec A.\vec B|\)

(b)

\(\frac{1}{2}|\vec A\times \vec B|\)

(c)

\(AB\sin\theta\)

(d)

\(AB\cos\theta\)

The displacement of the particle along a straight line at time t is given by X = a + bt + ct² where a, b, c are constants. The acceleration of the particle is ______________.

(a)

a

(b)

b

(c)

c

(d)

2c

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 the correct statement from the following

(a)

Centrifugal and centripetal forces are action reaction pairs

(b)

Centripetal forces is a natural force

(c)

Centrifugal force arises from gravitational force

(d)

Centripetal force acts towards the center and centrifugal force appears to act away from the center in a circular motion.

Unit of momentum _______________.

(a)

kg ms^-2

(b)

kg ms^-1

(c)

M L T^-2

(d)

M L T^-1

Due to the action of internal forces of the system, the total linear momentum of the system is ____________.

(a)

a variable

(b)

a constant

(c)

always zero

(d)

always infinity

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

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

\({{1}\over{2}}{m}{v}^{2}\)

(b)

mv³

(c)

\({{1}\over{2}}{m}{v}^{3}\)

(d)

\({{1}\over{2}}{m}{v}^{2}\)

The kinetic energy acquired by a mass m in travelling distance d, starting from rest, under the action of a constant force is directly proportional to _____________.

(a)

m

(b)

m⁰

(c)

\(\sqrt m\)

(d)

\(\frac{1}{\sqrt m}\)

1 kilowatt-hour is equivalent to _____________.

(a)

10^-7 J

(b)

1.6\(\times\)10^-19 J

(c)

4.186 J

(d)

3.6\(\times\)10^-6 J

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 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/\(\sqrt{2}\)

The radius of gyration of a solid sphere of radius r about a certain axis is r. The distance of that axis from the centre of the sphere is ___________.

(a)

\(\frac { 2 }{ 5 } \)r

(b)

\(\sqrt { \frac { 2 }{ 5 } } \)r

(c)

\(\sqrt { 0.6 } \)r

(d)

\(\sqrt { \frac { 5 }{ 3 } } \)r

The unit of torque is _______________.

(a)

Js

(b)

Nm^-2

(c)

Nm

(d)

Js^-1

The linear momentum and position vector of the planet is perpendicular to each other at

(a)

perihelion and aphelion

(b)

at all points

(c)

only at perihelion

(d)

no point

The work done by Sun on Earth at any finite interval of time is

(a)

Positive, negative or zero

(b)

Strictly positive

(c)

Strictly negative

(d)

It is always zero

A liquid is contained in a vertical tube of semicircular cross section the contact angel is zero. The force of surface tension on the curved part & on the flat part are in ratio ______________.

(a)

1 : 1

(b)

1 : 2

(c)

\(\pi\)  : 2 

(d)

2 : \(\pi\)

The period of Moon's rotation around the Earth is nearly 29 days. If Moon's mass were 2 fold its present value and all other things remained unchanged the period of Moon's rotation would be nearly _________ days.

(a)

29\(\sqrt{2}\)

(b)

\(\frac{29}{\sqrt{2}}\)

(c)

29 x 2

(d)

29

If a wire is stretched to double of its original length, then the strain in the wire is

(a)

1

(b)

2

(c)

3

(d)

4

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

The breaking stress of a wire depends upon __________.

(a)

length of the wire

(b)

material of the wire

(c)

radius of the wire

(d)

shape of the cross-section

When a fluid passes through the constricted part of a pipe, its _________.

(a)

velocity and pressure decrease

(b)

velocity and pressure increase

(c)

velocity decreases and pressure increases

(d)

velocity increases and pressure decreases

The graph between volume and temperature in Charles’ law is

(a)

an ellipse

(b)

a circle

(c)

a straight line

(d)

a parabola

A hot cup of coffee is kept on the table. After some time it attains a thermal equilibrium with the surroundings. By considering the air molecules in the room as a thermodynamic system, which of the following is true

(a)

ΔU > 0, Q = 0

(b)

ΔU > 0, W < 0

(c)

ΔU > 0, Q > 0

(d)

ΔU = 0, Q > 0

A process in which the temperature of working substance remains constant during its expansion or compression ____________________.

(a)

isothermal

(b)

adiabatic

(c)

isobaric

(d)

isochoric

Two metal rods A and B are having their initial lengths in the ratio 2 : 3, and coefficients of linear expansion in the ratio 3 : 4. When they are heated through same temperature difference, the ratio of their linear expansions is  _______

(a)

1 : 2

(b)

2 : 3

(c)

3 : 4

(d)

4 : 3

A container has one mole of monoatomic ideal gas. Each molecule has f degrees of freedom. What is the ratio of \(\gamma =\frac { { C }_{ p } }{ { C }_{ V } } \) 

(a)

f

(b)

\(\frac{f}{2}\)

(c)

\(\frac{f}{f+2}\)

(d)

\(\frac{f+2}{f}\)

Which of the following shows the correct relationship between the pressure and density of an ideal gas at constant temperature?

(a)

(b)

(c)

(d)

The temperature of an ideal gas is increased from 27°C to 927°C. The root mean square speed of its molecules becomes ________________.

(a)

3 times

(b)

double

(c)

4 times

(d)

6 times

On colliding with the walls in a closed container, the ideal gas molecules _______________

(a)

transfer momentum to the walls

(b)

lose momentum completely

(c)

move with smaller speeds

(d)

perform Brownian motion.

The length of a second’s pendulum on the surface of the Earth is 0.9 m. The length of the same pendulum on surface of planet X such that the acceleration of the planet X is n times greater than the Earth is

(a)

0.9n

(b)

\(\frac{0.9}{n}\)m

(c)

0.9n²m

(d)

\(\frac{0.9}{n^2}\)

Two bodies A and B whose masses are in the ratio 1:2 are suspended from two separate massless springs of force constants k_A and k_B respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio 1:2, the ratio of the amplitude A to that of B is

(a)

\(\sqrt { \frac { { K }_{ B } }{ { 2 }K_{ A } } } \)

(b)

\(\sqrt { \frac { { K }_{ B } }{ { 8 }K_{ A } } } \)

(c)

\(\sqrt { \frac { {2 K }_{ B } }{ { }K_{ A } } } \)

(d)

\(\sqrt { \frac { {8 K }_{ B } }{ { }K_{ A } } } \)

The phase difference between the unstantaneous velocity & acceleration of a particle executing simple harmonic motion is ________________.

(a)

0.5 π

(b)

π

(c)

0.707π

(d)

0.61 m

The maximum displacement of a particle executing SHM is 1 cm and the maximum acceleration is (1.57)² cm/s². Its time period is __________.

(a)

0.25 s

(b)

4.0 s

(c)

1.57 s

(d)

3.14 s

For a particular tube, among six harmonic frequencies below 1000 Hz, only four harmonic frequencies are given: 300 Hz, 600 Hz, 750 Hz and 900 Hz. What are the two other frequencies missing from this list?

(a)

100 Hz, 150 Hz

(b)

150 Hz, 450 Hz

(c)

450 Hz, 700 Hz

(d)

700 Hz, 800 Hz

Which of the following options is correct?.

A	B
(1) Quality	(A) Intensity
(2) Pitch	(B) Waveform
(3) Loudness	(C) Frequency

Options for (1), (2) and (3), respectively are

(a)

(B), (C) and (A)

(b)

(C), (A) and (B)

(c)

(A), (B) and (C)

(d)

(B), (A) and (C)

Speed of sound wave in air _____________.

(a)

Independent of temp

(b)

Increase with pressure

(c)

Increase with increase in humidity

(d)

Decreases with increase in humidity

Length of a string tied to two rigid supports is 40 cm maximum length of a stationary wave produced on it is ___________.

(a)

20

(b)

80

(c)

40

(d)

120