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Question: A body of mass m moving along a straight line collides with a body of mass nm which is also moving w...

A body of mass m moving along a straight line collides with a body of mass nm which is also moving with a velocity kv in the same direction. If the first body comes to rest after the collision, then the velocity of second body after the collision would be

A

nv(1+nk)\frac{nv}{(1 + nk)}

B

nv(1−nk)\frac{nv}{(1 - nk)}

C

(1−nk)vn\frac{(1 - nk)v}{n}

D

(1+nk)vn\frac{(1 + nk)v}{n}

Answer

(1+nk)vn\frac{(1 + nk)v}{n}

Explanation

Solution

Initial momentum = mv+nm(kv)mv + nm(kv)

and final momentum =0+nmV= 0 + nmV

By the conservation of momentum,

mv+nm(kv)=0+nmVmv + nm(kv) = 0 + nmV

⇒ v+nkv=nVv + nkv = nV ⇒ nV=(1+nk)vnV = (1 + nk)v ⇒ V=(1+nk)vnV = \frac{(1 + nk)v}{n}