A body of mass m moving with a certain speed suffers an inelastic collision with a body of mass M at rest. The ratio of the final kinetic energy of the system to the initial kinetic energy is

Options

A. `m/(m + M)`
B. `M/(m + M)`
C. `(m + M)/m`
D. `(m + M)/M`

Answer

A

Explanation

Initial momentum of the system=mv, since body of mass M is at rest. After the inelastic collion, the bodies stick together and the mass of the composite body is (m+M). IfV is the speed of the composite body, its momentum will be (m+M)V. From the principle of conservation of momentum
we have , `mv = (m + M)V " or " V = ((m)/(m + M))v`
Intial K.E. = `1//2 mv^2 ` Final KE = `1//2 (m + M) V^2`
`("Final KE")/("Intial KE") = ((m + M)V^2)/(mv^2) = m/(m + M) [because V = ((m)/(m + M))v]`