If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be

(a)

8%

(b)

2%

(c)

4%

(d)

6%

If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms^-2) 

(a)

77.3 m

(b)

78.4 m

(c)

80.5 m

(d)

79.2 m

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

(a)

Gravitational force exerted by Earth on the book

(b)

Gravitational force exerted by the book on Earth

(c)

Normal force exerted by the book on the table

(d)

None of the above

The work done by the conservative force for a closed path is

(a)

always negative

(b)

zero

(c)

always positive

(d)

not defined

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 gravitational potential energy of the Moon with respect to Earth is

(a)

always positive

(b)

always negative

(c)

can be positive or negative

(d)

always zero

For a given material, the rigidity modulus is \(\left( \frac { 1 }{ 3 } \right) \)^rd of Young’s modulus. Its Poisson’s ratio is

(a)

0

(b)

0.25

(c)

0.3

(d)

0.5

When a cycle tyre suddenly bursts, the air inside the tyre expands. This process is

(a)

isothermal

(b)

adiabatic

(c)

isobaric

(d)

isochoric

An ideal gas is maintained at constant pressure. If the temperature of an ideal gas increases from 100K to 1000K then the rms speed of the gas molecules

(a)

increases by 5 times

(b)

increases by 10 times

(c)

remains same

(d)

increases by 7 times

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)

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