Question

an object of mass M moving with velocity V makes an head-on collision with a body of mass m initially at rest. after the collision the velocity of the object of mass M along its original direction equals v/n. obtain an expression for the ratio m/M​

Answer 1

acc to law of conservation of momentum

MV + m(0) = (M+m)v

[because if 2nd body was at rest both bodies will move together as one body after collision]

MV= (M+m)v

MV = Mv + mv

M (V-v) = mv

M/m =v /(V-v)

m/M = (V-v) /v

now v = V/n

so

m/M = (V-(V/n)) / (V/n)

m/M = V (1-(1/n)) / (V/n)

after solving

m/M = n-1

Hope this helps :)