A particle of mass m is moving with speed 2 v and collides with a mass 2 m moving with speed v in the same…

1. $\sqrt{2}\text{v}$
2. $\frac{\text{v}}{\sqrt{2}}$
3. $2\sqrt{2}\text{v}$
4. $\frac{\text{v}}{\left(2\sqrt{2}\right)}$

Solution

As $2\mathrm{m}$ splits into equal parts, ${\mathrm{v}}_1={\mathrm{v}}_2$ and $\mathrm{\theta }=45^0$
From conservation of linear momentum,
$\mathrm{m}\left(2\mathrm{v}\right)+2\mathrm{m}\left(\mathrm{v}\right)=2\left[\mathrm{m}{\mathrm{v}}_1\cos 45^{\mathrm{o}}\right]$
$\Rightarrow {\mathrm{v}}_1={\mathrm{v}}_2=2\sqrt{2}\text{v}$

Asked in: JEE Main 2019 (09 Apr Shift 2)

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