A 20 kg ball moving with a velocity 6 m/s collides with a 30 kg ball initially at rest. If both of them coalesce, then the final velocity of the combined mass is

• 6 m/s

• 5 m/s

• 3.6 m/s

• 2.4 m/s

A car of mass 1000 kg moves on a circular track of radius 20 m. If the coefficient of friction is 0.64, then the maximum velocity with which the car can move is

• 15 m/s

• 11.2 m/s

• 20 m/s

• 18 m/s

A player caught a cricket ball of mass 150 g moving at the rate of 20 ms^-1. If the catching process be completed in 0.1 s, the force of the blow exerted by the ball on the hands of the player is

• 0.3 N

• 30 N

• 300 N

• 3000 N

A uniform metal chain is placed on a rough table such that one end of it hangs down over the edge of the table. When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is

• $\frac{3}{4}$

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{1}{3}$

In the motion of a rocket, physical quantity which is conserved is

• angular momentum

• linear momentum

• force

• work

Physical independence of force is a consequence of

• third law of motion

• second law of motion

• first law of motion

• all of these laws

The kinetic energy of a body becomes four times its initial value. The new momentum will be

• same as the initial value

• twice the initial value

• thrice the initial value

• four times the initial value

An ice cart of mass 60 kg rests on a horizontal snow patch with coefficient of static friction $\frac{1}{3}$. Assuming that there is no vertical acceleration, find the magnitude of the maximum horizontal force required to move the ice cart. (g = 9.8 ms^-2)

• 100 N

• 110 N

• 196 N

• 206 N

79.

A cyclist is moving in a circular track of radius 80 m with a velocity v = 36 km/h. He has to lean from the vertical approximately through an angle : (Take g = 10 ms^-2)

• ${\tan }^{-1} \left(4\right)$

• ${\tan }^{-1} \left(\frac{1}{3}\right)$

• ${\tan }^{-1} \left(\frac{1}{8}\right)$

• ${\tan }^{-1} \left(2\right)$

A car is racing on a circular track of 180 m radius with a speed of 32 ms^-1. What should be the banking angle of the road to avoid changes of skidding of the Vehicle at this speed without taking into consideraion the friction between the tyre and the road ?

• 45°

• 60°

• 30°

• 15°