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?

A truss consists of horizontal members (AC, CD, DB and EF) and vertical members (CE and DE) having length 1 each. The members AE, DE and BF are inclined at $${45^0}$$ to the horizontal. For the uniformly distributed load ‘p’ per unit length on the member EF of the truss shown in figure given below, the force in the member CD 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

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