A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass ‘M’ initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance ‘s’ along the floor. Assuming $$\mu $$ to be the coefficient to kinetic friction between the block and the floor and ‘g’ the acceleration due to gravity what is the velocity v of the bullet?

The ratio of tension on the tight side to that on the slack side in a flat belt drive is

A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll the wheel along the rail is

A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is