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

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

A cylinder is released from rest from the top of an incline of inclination theta and length 'L'. If the cylinder rolls without slipping. What will be its speed when it reaches the bottom?

A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take in reaching the ground?

Two friends A and B (each weighing 40 kg ) are sitting on a frictionless platform some distance d apart. A rolls a ball of mass 4 kg on the platform towards B which B catches. Then B rolls the ball towards A and A catches it. The ball keeps on moving back and forth between A and B . The ball has a fixed speed of 5 m//s on the platform. a. Find the speed of A after he rolls the ball for the first time. b. Find the speed of A after he catches the ball for the first time. c. Find the speed of A and B after the ball has made five round trips and is held by A . d. How many times can A roll the ball? e. Where is the centre of mass of the system A + B + ball at. the end of the nth trip?

A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/s, then the rate (in cm/s) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is

Water leaks out from an open tank through a hole of area 2mm^2 in the bottom. Suppose water is filled up to a height of 80 cm and the area of cross section of the tankis 0.4 m^2 . The pressure at the open surface and the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank. a. Find the initial speed of water coming out of the hole. b. Findteh speed of water coming out when half of water has leaked out. c. Find the volume of water leaked out during a time interval dt after the height remained is h. Thus find the decrease in height dh in term of h and dt. d. From the result of part c. find the time required for half of the water to leak out.

A sphere starts rolling down can incline of inclination theta. Find the speed of its centre when it has covered a distance l.

A ball is thrown vertically upward at a speed of 10 m/s. When it has reached one half of its maximum height. How high does the ball rise? (g=10ms^(-2) )

A ladder 17 metre long is leaning against the wall. The base of the ladder is pulled away from the wall at a rate of 5m/s. When the base of the ladder is 8 metres from the wall. How fast is the top of the ladder moving down the wall?