A body of mass 5 Kg is moving along the X-axis with velocity $2 {ms}^{- 1}$ . Another body of mass 10kg is moving along the Y-axis with a velocity $\sqrt{3} {ms}^{- 1}$ . They collide at the origin and stick together. The final velocity of the combined mass is

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$\sqrt{3} m s^{- 1}$

$\frac{4}{3} {ms}^{- 1}$

$\frac{5}{3} m s^{- 1}$

$(\sqrt{3} + 1) m s^{- 1}$

answer is C.

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Detailed Solution

Applying conservation of momentum

$m_{1} u_{1} \hat{i} + m_{2} u_{2} \hat{j} = (m_{1} + m_{2}) V_{C}$

$(5 \times 2) \hat{i} + (10 \times \sqrt{3}) \hat{j} = 15 V_{C}$

$\frac{\sqrt{10^{2} + {(10 \sqrt{3})}^{2}}}{15} = V_{C}$ = $\frac{4}{3} {ms}^{- 1}$

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