A mass ' $M$ ' moving with velocity ' $\mathrm{V}$ ' along $\mathrm{x}$-axis collides and sticks to another…

A mass ' $M$ ' moving with velocity ' $\mathrm{V}$ ' along $\mathrm{x}$-axis collides and sticks to another mass $2 \mathrm{M}$ which is moving along $\mathrm{Y}$-axis with velocity ' $3 \mathrm{~V}$ '. The velocity of the combination after collision is
  1. $\frac{V}{3} \hat{i}+2 V \hat{j}$
  2. $\frac{V}{2} \hat{\mathrm{i}}+\mathrm{V} \hat{\mathrm{j}}$
  3. $\frac{V}{3} \hat{\mathrm{i}}-2 \mathrm{~V} \hat{\mathrm{j}}$
  4. $\frac{V}{2} \hat{\mathrm{i}}-\mathrm{V} \hat{\mathrm{j}}$

Solution

From law of conservation of linear momentum, $\begin{aligned} & M v \hat{i}+2 M(3 v \hat{j})=3 M \vec{v} \\ & v \hat{i}+6 v \hat{j}=3 \vec{v} \\ & \vec{v}=\frac{v}{3} \hat{i}+2 v \hat{j} \end{aligned}$ .

Asked in: MHT CET 2023 (10 May Shift 2)

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