Two spherical bodies of the same mass M are moving with velocities `v_1 and v_2`. These collide perfectly inelastically, then the loss of KE due to collision is

Options

A. `1/2 M (v_1 - v_2)^2`
B. `1/2 M (v_1^2 - v_2^2)`
C. `1/4 M(v_1 - v_2)^2`
D. `2M(v_1^2 - v_2^2)`

Answer

C

Explanation

Loss of kinetic energy= `1/2 (m_1 m_2)/((m_1 + m_2)) (v_1 + v_2)^2 = 1/2 (M xx M)/((M xx M)) (v_1 - v_2)^2 = M/4 (v_1 - v_2)^2`