Two bodies A and B of masses 2 m and m are projected vertically upwards from the ground with velocities u and 2 u respectively. The ratio of the kinetic energy of body A and the potential energy of body B at a height equal to half of the maximum height reached by body A is

Step-by-step solution

For body A, H _ = u ^2 2 ~g , ~m ₁=2 ~m , u ₁= u , H ₁= H _ 2 = u ^2 4 ~g By principle of energy conservation, 1 2 m₁ u₁^2=m₁ gH ₁+( KE )_ A ( KE )_ A = 1 2 (2 ~m ) u ^2-(2 ~m ) g ( u ^2 4 ~g )= 1 2 mu ^2 For body B , H ₂= u ^2 4 ~g , ~m ₂= m , u ₂=2 u ( P.E )_ B = m ₂ gH ₂= mg ( u ^2 4 ~g )= 1 4 mu ^2 ( KE )_ A ( PE )_ B = 1 2 mu ^2 1 4 mu ^2 =2: 1