Two identical mass M moving with velocity `u_1 and u_2` collide perfectly inelastically. The loss in kinetic energy is

Options

A. `M/2 (u_2 - u_1)^2`
B. `M/2 (u_1^2 - u_2^2)`
C. `M/4 (u_2 - u_1)^2`
D. `M/4 (u_1^2 - u_2^2)`

Answer

C

Explanation

Loss in kinetic energy in a perfectly inelastic collision is
`Delta K = 1/2 (m_1m_2)/((m_1 + m_2)) (u_1 - u_2)^2`
Here, `m_1 = m_2 = M`
`:. Delta K = 1/2(M xx M)/((M + M)) (u_1 - u_2)^2 = M/4 (u_1 - u_2)^2` .