A body of mass 2   k g makes an elastic collision with a second body at rest and continues to move in…

1. $1.8\mathrm{ }\mathrm{k}\mathrm{g}$
2. $1.2\mathrm{ }\mathrm{k}\mathrm{g}$
3. $1.0\mathrm{ }\mathrm{k}\mathrm{g}$
4. $1.5\mathrm{ }\mathrm{k}\mathrm{g}$

Solution

From conservation of linear momentum
$\mathrm{m}\mathrm{U}=\mathrm{m}\frac{\mathrm{U}}{4}+\mathrm{M}\mathrm{V}$ . . . (i)
For elastic collision: $\mathrm{e}=1=\frac{\mathrm{V}-\frac{\mathrm{U}}{4}}{\mathrm{u}}$
$\mathrm{V}=\frac{5\mathrm{U}}{4}$ . . . (ii)
From equation (i) & (ii),
$\mathrm{m}\mathrm{U}=\mathrm{m}\frac{\mathrm{U}}{4}+\mathrm{M}\left(\frac{5\mathrm{U}}{4}\right)$
$\mathrm{m}=\frac{\mathrm{m}}{4}+\frac{5}{4}\mathrm{M}\mathrm{ }\mathrm{ }\Rightarrow \mathrm{M}=\frac{3\mathrm{m}}{5}=1.2\mathrm{ }\mathrm{k}\mathrm{g}$

Asked in: JEE Main 2019 (09 Apr Shift 1)

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