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

The amount of work done by the centripetal force on the object moving in a circular path is ______________.

(a)

zero

(b)

infinity

(c)

positive

(d)

negative

The kinetic energy is not conserved in ______________.

(a)

Elastic collision

(b)

Inelastic collision

(c)

both (a) and (b)

(d)

none

For inelastic collision co-efficient of restitution is ______________.

(a)

0

(b)

1

(c)

0 < e < 1

(d)

\(\infty \)

If the momentum of a body increases by 25% its kinetic energy will increase by _____________.

(a)

25%

(b)

50%

(c)

125%

(d)

56.25%

A boy "A" of mass 50 kg climbs up a staircase in 10 s. Another boy "B" of mass 60 kg climbs up the same staircase in 15s. The ratio of the power developed by the boys "A" and "B" is ____________.

(a)

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

(b)

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

(c)

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

(d)

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

Two bodies of masses 2 kg and 3 kg have position vectors \(\hat { i } +2 \hat { j} +\hat { k} \) and \(\hat { -4i } - \hat {(-3j)} +\hat { 6k} \) respectively. The centre of mass of this system has a position vector _____________.

(a)

\(\hat {- 3i } -\hat { j}\)

(b)

\(\hat {5 i } - \hat { j} +2\hat { k} \)

(c)

\(\hat {-2 i } - \hat { j} +4\hat { k} \)

(d)

\(\hat { -3i } - \hat { j} +\hat7 { k} \)

A couple produces____ motion.

(a)

linear and rotational

(b)

purely rotational

(c)

purely linear

(d)

no

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

The ratio of the radius of gyration of a circular disc to that of circular ring, each of same mass and same radius about their axes is ______________.

(a)

\(\sqrt{3}:\sqrt{2}\)

(b)

\(1:\sqrt{2}\)

(c)

\(\sqrt{2}:1\)

(d)

\(\sqrt{2}:\sqrt{3}\)

Moment of inertia of a uniform solid cylinder about an axis passing through the center and along the axis of the cylinder is _______________.

(a)

MR²

(b)

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

(c)

\(\frac { 1 }{ 2 } \)MR²

(d)

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

A solid floats in a liquid in a partially dipped position ______________.

(a)

The solid exerts a force equal to its weight on the liquid

(b)

The liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid

(c)

The weight of the displaced liquid equals the weight of the solid

(d)

All the above

The force of viscosity is ___________.

(a)

electro magnetic

(b)

gravitational

(c)

nuclear

(d)

weak

What is an ideal fluid?

(a)

A fluid which has no viscosity

(b)

A fluid which is incompressible

(c)

A fluid which has no surface tension

(d)

All the above

The pressure in a water tap at the base of a building is 3 x 10⁶ dynes/cm/ and on its top it is 1.6 x 10⁶ dynes/cm². The height of the building is approximately  __________.

(a)

7 m

(b)

14 m

(c)

70 m

(d)

140 m

The dimensional formula of coefficient of viscosity is ________.

(a)

M⁰ L^-1 T^-1

(b)

M⁰ L² T^-1

(c)

ML² T^-1

(d)

ML^-1 T^-1

C_v & C_P  denote the molar specific heat capacities of a gas at constant volume and constant pressure then ________________.

(a)

C_p - C_v is larger for a diatomic ideal gas than for a monoatomic ideal gas

(b)

C_p, + C_v is larger for a diatomic ideal gas than for a monoatomic ideal gas

(c)

C_p, / C_v is larger for a diatomic ideal gas than for a monoatomic ideal gas

(d)

C_p, x C_v is lesser for a diatomic ideal gas than for a monoatomic ideal gas

An adiabatic process is one in which __________________.

(a)

the change in internal energy is equal to the mechanical work done

(b)

the temperature of the gas change

(c)

no heat enters or leaves the gas

(d)

all of the above

A perfect gas at 27°C is heated at constant pressure so as to double its volume. The temperature of the gas becomes _____________.

(a)

54°C

(b)

150K

(c)

327°C

(d)

327K

Boyles' law is applicable in _______.

(a)

isochoric process

(b)

isothermal process

(c)

isobaric process

(d)

both (a) and (b)

One mole of gas occupies a volume of 200 ml. at 100 mm pressure. What is the volume occupied by two moles of this gas at 400 mm pressure and at same temperature?

(a)

50 ml

(b)

100 ml

(c)

200 ml

(d)

400 ml

The speeds of 5 molecules of a gas (in arbitrary units) are as follows: 2, 3, 4, 5, 6 The root mean square speed for these molecule is _________________.

(a)

2.91

(b)

3.52

(c)

4.00

(d)

4.24

In order to double the period of a simple pendulum _______.

(a)

its length should doubled

(b)

its length should be quadrupled

(c)

the mass of its bob should be doubled

(d)

the mass of its bob should be quadrupled.

The velocity of a particle, undergoing SHM is v at the mean position. If its amplitude is doubled, the velocity at the mean position will be  _______.

(a)

2 v

(b)

3 v

(c)

2\(\sqrt{2}v\)

(d)

4 v

Masses m_A and m_B hanging from the ends of strings of lengths I_A and I_B are executing. Simple harmonic motions. If their frequencies are related as f_A= 2/_B then ________.

(a)

I_A= 2/_B and m_A= m_B/2

(b)

I_A = 4/_B regardless of masses

(c)

l_A = I_B/4 regardless of masses.

(d)

I_A = 2/_B and m_A = 2m_B