Question

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision, their final velocities are V and v respectively. The value of v is

• A. $\frac{2 u M}{m}$
• B. $\frac{2 u M}{M}$
• C. $\frac{2 u}{1+\frac{m}{M}}$
• D. $\frac{2 u}{1+\frac{M}{m}}$

Answer 1

Answer: (C)

$\frac{2 u}{1+\frac{m}{M}}$

Answer 2

By law of conservation of momentum, Mu = MV + mv $\ldots\left(1\right)$
Also e= $\frac{\left|v_{1}-v_{2}\right|}{\left|u_{1}-u_{2}\right|} \, \Rightarrow \quad Mu=Mv-MV ....\left(ii\right)$
From (i) and (ii), 2Mu = (M + m)v
$\Rightarrow\quad v=\frac{2 uM}{M+m} \, \Rightarrow\quad v=\frac{2 u}{1+\frac{m}{M}}$