A body of mass m is moving towards the east and another body of equal mass is moving towards the north. If after collision both stick together, their speed after collision would be :

• v

• v/2

• $\sqrt{2}\mathrm{v}$

• $\frac{\mathrm{v}}{\sqrt{2}}$

A body of mass 1 kg is moving in a vertical circular path of radius 1 m. The difference between the kinetic energies at its highest and lowest position is :

• 20 J

• 10 J

• $4\sqrt{5} \mathrm{J}$

• 10($\sqrt{5}$ - 1) J

Two bodies are thrown up at angles of 40° and 60°, respectively, with the horizontal. If both bodies attain the same vertical height, then the ratio of velocities with which these are thrown is:

• $\sqrt{\frac{2}{3}}$

• $\frac{2}{\sqrt{3}}$

• $\sqrt{\frac{3}{2}}$

• $\frac{\sqrt{3}}{2}$

Escape velocity from a planet is v, If its mass is increased to 8 times and its radius is increased to 2 times, then the new escape velocity would be :

• v_e

• $\sqrt{2}$v_e

• 2v_e

• $2\sqrt{2}$v_e

A body takes time t to reach the bottom of an inclined plane of angle 0 with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is:

• $\frac{3}{4}\mathrm{tan\theta }$

• $\frac{2}{3}\mathrm{tan\theta }$

• $\frac{1}{4}\mathrm{tan\theta }$

• $\frac{1}{2}\mathrm{tan\theta }$

6.

Acceleration due to gravity:

• decreases from the equator to poles

• decreases from poles to the equator

• is maximum at the centre of the earth

• is maximum at the equator

Two bodies having masses m₁ = 40g and m₂ = 60 g are attached to the ends of a string of negligible mass and suspended from a massless pulley. The acceleration of the bodies is:

• 1 m/s²

• 2 m/s²

• 0.4 m/s²

• 4 m/s²

A block is moving up an inclined plane of inclination 60° with a velocity of 20 m/s and stops after 2 s. If g = 20 m/s² then the approximate value of the coefficient of friction is :

• 3

• 3.3

• 0.27

• 0.33

A coin placed on a rotating turntable just slips if it is placed at a distance of 8 cm from the centre. If angular velocity of the turntable is doubled, it will just slip at a distance of :

• 1 cm

• 2 cm

• 4 cm

• 8 cm

When a man increases his speed by 2 m/s, he finds that his kinetic energy is doubled, the original speed of the man is :

• $2(\sqrt{2} - 1) \mathrm{m}/\mathrm{s}$

• $2(\sqrt{2} + 1) \mathrm{m}/\mathrm{s}$

• 4.5 m/s

• none of these