A particle of mass m with an initial velocity collides perfectly elastically with a mass 3 m at rest. It moves with a velocity

Question

A particle of mass m with an initial velocity $u\hat{\text{i}}$ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity $v\hat{\text{j}}$after collision, then, vv is given by  

a)  $v=\sqrt{\frac{2}{3}}u$ 

b)  $v=\frac{u}{\sqrt{3}}$ 

c)  $v=\frac{u}{\sqrt{6}}$ 

d)  $v=\frac{u}{\sqrt{2}}$

Answer 1

The correct answer is option d) $v=\frac{u}{\sqrt{2}}$ 

Explaination ::

 

$mu\hat{i}+0=mv\hat{j}+3m\widehat{v^{\prime }}$

$\widehat{v^{\prime }}=\frac{u}{3}\hat{i}-\frac{v}{3}\hat{j}$  

$\frac{1}{2}m{u}^2=\frac{1}{2}m{v}^2+\frac{1}{2}(3m)((\frac{u}{3}{)}^2+(\frac{v}{3}{)}^2)$   --------{ K.E.}

$m{u}^2=m(v^2+(\frac{u^2}{3}+\frac{v^2}{3})$

$u^2=(v^2+\frac{u^2}{3}+\frac{v^2}{3})$

$3u^2-3v^2=u^2+v^2$

$2u^2=4v^2$

$u^2=2v^2$

$v=\frac{u}{\sqrt{2}}$