On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle $$\theta $$ to its initial direction and has a speed $${v \over 3}.$$ The second block's speed after the collision is

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 $$ \times $$ 10³ kg/m³ and g = 10 m/s² then the power (in watt) is

Two similar springs P and Q have spring constants K_P and K_Q, such that K_P > K_Q. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs W_P and W_Q are related as, in case (a) and case (b) respectively

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is