Question

A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embedded into it. The kinetic energy of the composite block will be 

(A) (1/2) mv² × [M / (m + m)] 

(B) (1/2) mv² × [(m + m) / M] 

(C) (1/2) MV² × [m / (m + M)] 

(D) (1/2) mv² × [m / (m + M)]

Answer 1

Correct option: (D) (1/2) mv² × [m / (m + M)]

Explanation:

by conservation of momentum,

(m)(v) + (M)(o) = (m + M)V

mv = (m + M)V

∴  V = {(mV) / (m + M)}

KE of composite block = (1/2) (M + m)V² 

= (1/2) (m + M) {(mV) / (m + M)}² 

= (1/2) {(m²v²) / (m + M)}

= (1/2)mv² × {m / (m +M)}