In the following, what are the quantities which that are conserved?

(a)

Linear momentum of planet

(b)

Angular momentum of planet

(c)

Total energy of planet

(d)

Potential energy of a planet

Viscosity is a property of ______________.

(a)

liquids only

(b)

solid only

(c)

solids & liquids only

(d)

liquids & gases only

A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

(a)

energy = 4 V T \(\left( \frac { 1 }{ r } -\frac { 1 }{ R } \right) \)is released

(b)

energy = 3 V T \(\left( \frac { 1 }{ r } +\frac { 1 }{ R } \right) \)is absorbed

(c)

energy = 3 V T \(\left( \frac { 1 }{ r } -\frac { 1 }{ R } \right) \)is released

(d)

energy is neither released nor absorbed

The molar specific heats of an ideal gas at a constant pressure & volume are denoted by Cp&Cv if r =\(\frac{C_{p}}{C_{v}}\) & R the universal gases constant then C_v is equal _____________.

(a)

\(\frac{1+r}{1-r}\)

(b)

\(\frac{R}{1-r}\)

(c)

\(\frac{r-1}{R}\)

(d)

rR

Two capillaries of lengths L & 2L and of radius R & 2R are connected in series the net rate of flow of fluid through them will (rate of the flow through singe capillary,\(x=\pi R^{4}/8 \eta L\)) be ____________.

(a)

\(\frac{8}{9}\alpha\)

(b)

\(\frac{9}{8}\alpha\)

(c)

\(\frac{5}{7}\alpha\)

(d)

\(\frac{7}{5}\alpha\)

The viscous force the relative motion between the adjacent layers of a fluid in motion which one of the following is absolutely fit?

(a)

opposes

(b)

never affects

(c)

facilitates

(d)

may effect under certain conditions

The weight of a body in air is 100 N. How much will it weight in water, if it displaces 400 cc of water?

(a)

90 N

(b)

94 N

(c)

98 N

(d)

None of these

At critical temperature the surface tension of a liquid ________.

(a)

is zero

(b)

is the same as that at any other temperature

(c)

is infinity

(d)

cannot be determined

In an isochoric process, we have

(a)

W = 0

(b)

Q = 0

(c)

ΔU = 0

(d)

ΔT = 0

In an adiabatic process, the state of a gas is changed from P₁' V₁' T₁' P₂' V₂' T₂ Which of the following relations is correct?

(a)

\({ T }_{ 1 }{ V }_{ 1 }^{ \gamma -1 }={ T }_{ 2 }{ V }_{ 2 }^{ \gamma -1 }\)

(b)

\({ P }_{ 1 }{ V }_{ 1 }^{ \gamma -1 }={ P }_{ 2 }{ V }_{ 2 }^{ \gamma -1 }\)

(c)

\({ T }_{ 1 }{ P }_{ 1 }^{ \gamma -1 }={ T }_{ 2 }{ P }_{ 2 }^{ \gamma }\)

(d)

\({ T }_{ 1 }{ V }_{ 1 }^{ \gamma -1 }={ T }_{ 2 }{ V }_{ 2 }^{ \gamma }\)

Which of the following will make the volume of an ideal gas four times?

(a)

double the absolute temperature and double the pressure

(b)

Halve the absolute temperature and double the pressure.

(c)

Quarter the absolute temperature at constant pressure.

(d)

Quarter the pressure at constant temperature.

An ideal gas is expanding such that PT2 = constant the coefficient of volume expansion of the gas is _____________.

(a)

\(\frac{1}{T}\)

(b)

\(\frac{2}{T}\)

(c)

\(\frac{3}{T}\)

(d)

\(\frac{4}{T}\)

During an adiabatic process, if the pressure of an ideal gas is proportional to the cube of its temperature, the ratio \(\gamma \)=\(\frac{C_P}{C_v}\) is_______.

(a)

2

(b)

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

(c)

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

(d)

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

Kinetic theory ___________.

(a)

Correctly explains specific heat capacities of many liquid

(b)

Correctly explains specific heat capacities of many gases

(c)

Correctly explains specific heat capacities of many solids

(d)

Correctly explains specific heat capacities of many super cooled liquid

A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is

(a)

T'= \(\sqrt{2}\)T

(b)

\(T'=\frac { T }{ \sqrt { 2 } } \)

(c)

T'=\(\sqrt{2T}\)

(d)

\(T'=\sqrt { \frac { T }{ 2 } } \)

A simple harmonic oscillator has a period of 0.01 s and an amplitude of 0.2 m. The magnitude of the velocity in m/s at the centre of oscillation is _________

(a)

20\(\pi\)

(b)

40\(\pi\)

(c)

60\(\pi\)

(d)

80\(\pi\)

The angular velocity and the amplitude of a simple pendulum are co and a, respectively. The ratio of its kinetic and potential energies at a displacement x from the mean position is ________.

(a)

\(\frac { { x }^{ 2 }{ \omega }^{ 2 } }{ { a }^{ 2 }-{ x }^{ 2 }{ \omega }^{ 2 } } \)

(b)

\(\frac { { x }^{ 2 } }{ { a }^{ 2 }-{ x }^{ 2 } } \)

(c)

\(\frac { { { a }^{ 2 }-x }^{ 2 }{ \omega }^{ 2 } }{ { x }^{ 2 }{ \omega }^{ 2 } } \)

(d)

\(\frac { { a }^{ 2 }-{ x }^{ 2 } }{ { x }^{ 2 } } \)

Which of the following functions represent SHM?
I. Y = sin ωt - cos ωt
II. y = sin³t
III. y = 5 cos\(\ \left( \frac { 3\pi }{ 4 } -3\omega t \right) \)
IV. y = 1 + ωt + ω²t²

(a)

I and III

(b)

I and II

(c)

only I

(d)

I, II and III

Let y = \(\frac{1}{1+x^2}\) at t = 0 s be the amplitude of the wave propagating in the positive x-direction. At t = 2 s, the amplitude of the wave propagating becomes \(y=\frac{1}{1+(x-2)^{2}}. \) Assume that the shape of the wave does not change during propagation. The velocity of the wave is

(a)

0.5m s^-1

(b)

1.0m s^-1

(c)

1.5m s^-1

(d)

2.0m s^-1

The fractional change in wavelength of light coming from a star is 0.014%. What is its velocity?

(a)

4.2\(\times\)10³ m/s

(b)

3.8\(\times\)10⁸ m/s

(c)

3.5\(\times\)10³ m/s

(d)

4.2\(\times\)10⁴ m/s

The speed of the wave represented by y =A sin(ωt - kx) is ________.

(a)

k/ω

(b)

ω/k

(c)

ωk

(d)

1/ωk

Ultrasonic waves are those waves which _______.

(a)

human beings cannot hear

(b)

human beings can hear

(c)

have high velocity

(d)

have large amplitude

If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity will _________.

(a)

increase by a factor of 2

(b)

decrease by a factor of 2

(c)

decrease by a factor of 4

(d)

remain unchanged

If v_a, v_h, and v_m are the speeds of sound in air, hydrogen and a metal at the same temperature, then _______

(a)

v_h>v_a>v_m

(b)

v_m>v_h>v_a

(c)

v_h>v_m>v_a

(d)

v_a>v_h>v_m

Doppler shift in frequency does not depend upon ________.

(a)

the actual frequency of the wave

(b)

the velocity of the source from the listener

(c)

the velocity of the source

(d)

the velocity of the observer.