A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km$h^{-1}$. The centripetal force is

(1) 250 N

(2) 750 N

(3) 1000 N

(4) 1200 N

Two bodies with kinetic energies in the ratio 4 : 1 are moving with equal linear momentum. The ratio of their masses is

(1) 1 : 2

(2) 1 : 1

(3) 4 : 1

(4) 1 : 4

Two masses $M_1=5 kg, M_2= 10 kg$ are connected at the ends of an inextensible string passing over a frictionless pulley as show. When masses are released, then acceleration of masses will be:

(1) g

(2) $\frac{g}{2}$

(3) $\frac{g}{3}$

(4) $\frac{g}{4}$

A particle of mass 1 kg is thrown vertically upwards with speed 100 m$s^{-1}$. After 5 s it explodes into two parts. One part of mass 400 g comes back with speed 25 m$s^{-1}$, what is the speed of other part just after an explosion?

(1) 100 m$s^{-1}$upward

(2) 600 m$s^{-1}$ upward

(3) 100 m$s^{-1}$ downward

(4) 300 m$s^{-1}$ upward

A stone is attached to one end of a string and rotated in a vertical circle. If string breaks at the position of maximum tension, it will break at:

(1) A

(2) B

(3) C

(4) D

A player takes 0.1 s in catching a ball of mass 150 g moving with velocity of 20 m$s^{-1}$. The force imparted by the ball on the hands of the player is:

(1) 0.3 N

(2) 3 N

(3) 30 N

(4)  300 N

A lift of mass 1000 kg which is moving with an acceleration of 1 m$s^{-2}$ in the upward direction, then the tension developed in the string which is connected to lift is

(1) 9800 N

(2) 10, 800 N

(3) 11, 000 N

(4) 10, 000 N

A block B is pushed momentarily along a horizontal surface with an initial velocity v. If $\mu$ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time

(1)  g$\mu$/v

(2) g/v

(3) v/g

(4) v/(g$\mu$)

Three forces acting on a body are shown in the figure below. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

(1) $\sqrt{3}N$

(2) 0.5 N

(3) 1.5 N

(4) $\frac{\sqrt{3}}{4} N$

A roller coaster is designed such that riders experience 'weightlessness' as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

(1) 13 m$s^{-1}$ and 14 m$s^{-1}$

(2) 14 m$s^{-1}$ and 15 m$s^{-1}$

(3) 15 m$s^{-1}$ and 16 m$s^{-1}$

(4) 16 m$s^{-1}$ and 17 m$s^{-1}$