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%

Identify the unit vector in the following?

(a)

\(\hat { i } +\hat { j } \)

(b)

\(\frac { \hat { i } }{ \sqrt { 2 } } \)

(c)

\(\hat { k } -\frac { \hat { j } }{ \sqrt { 2 } } \)

(d)

\(\frac { \hat { i } +\hat { j } }{ \sqrt { 2 } } \)

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

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 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

If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be

(a)

64.5

(b)

1032

(c)

182.5

(d)

730

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 uniform rod is heated, which of the following quantity of the rod will increase

(a)

mass

(b)

weight

(c)

center of mass

(d)

moment of inertia

The average translational kinetic energy of gas molecules depends on

(a)

number of moles and T

(b)

only on T

(c)

P and T

(d)

P only

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