A ball, intially at the top of the inclined hill, is allowed to roll down. At the bottom its speed is 4 m/s. Next the ball is again rolled down the hill, but this time it does not start from rest. It has an initial speed of 3 m/s. How fast is it going when it gets to the bottom ?

A solid cylinder rolls up an inclined plane of angle of inclination 30° . At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 m/s. (a) How far will the cylinder go up the plane? (b) How long will it take to return to the bottom?

A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

When a point mass slips down a smooth incline from top, it reaches the bottom with linear speed v. If same mass in the form of disc rolls down without slipping a rough incline of identical geometry through same distance, what will be its linear velocity at the bottom ?

A hoop of radius 2 m weights 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stope it?

A spherical ball of mass 20 kg is stationary at the top of the hill of height 100 m . It rolls down smooth surface to ground then climb up another hill of height 40 m and finally rolls down to a horizontal base at a height of 15 m above the ground . The maximum velocity attained by a ball is ....... ( g = 9.8 m//s^(2))

A solid sphere of diameter 0.1 m and 5 kg is rolling down an inclined plane with a speed of 4 m/s. The total kinetic energy of the sphere is :

A rocket is moving in a gravity free space with a constant acceleration of 2 m//s^(2) along + x direction (see figure). The length of a chamber inside the rocket is 4 m . A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3 m//s relative to the rocket . At the same time , another ball is thrown in + x direction with a speed of 0.2 m//s drom its right end relative to the rocket . The time in seconds when the two balls hit each other is

A large , heavy box is sliding without friction down a smooth plane of inclination theta . From a point P on the bottom of the box , a particle is projected inside the box . The initial speed of the particle with respect to the box is u , and the direction of projection makes an angle alpha with the bottom as shown in Figure . (a) Find the distance along the bottom of the box between the point of projection p and the point Q where the particle lands . ( Assume that the particle does not hit any other surface of the box . Neglect air resistance .) (b) If the horizontal displacement of the particle as seen by an observer on the ground is zero , find the speed of the box with respect to the ground at the instant when particle was projected .

A ball is dropped from the top of a building the ball takes 0.5 s to fall past the 3 m length of a window at certain distance from the top of the building. Speed of the ball as it crosses the top edge of the window is (g=10 m//s^(2))