Three masses m , 2 m and 3 m are moving in x − y plane with speed 3 u , 2 u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of r

Question

Three masses m , 2 m and 3 m are moving in x − y plane with speed 3 u , 2 u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be:

TestHub · Accepted Answer

From the law of conservation of momentum we know that, $m_{1} u_{1} + m_{2} u_{2} + \dots . = m_{1} v_{1} + m_{2} v_{2} + \dots .$ Given $m_{1} = m, m_{2} = 2 m$ and $m_{3} = 3 m$ and $u_{1} = 3 u, u_{2} = 2 u$ and $u_{3} = u$ Let the velocity when they stick $= v$ $Then, according to question,$
$m \times 3 u (\hat{i}) + 2 m \times 2 u (- \hat{i} cos 6 0^{\circ} - \hat{j} sin 6 0^{\circ}) + 3 m \times u (- \hat{i} cos 6 0^{\circ} + \hat{j} sin 6 0^{\circ}) = (m + 2 m + 3 m) v \Rightarrow 3 m u \hat{i} - 4 mu \frac{i ^}{2} - 4 mu (\frac{3}{2} \hat{j}) - 3 mu \frac{i ^}{2} + 3 m u (\frac{3}{2} \hat{j}) = 6 m v \Rightarrow m u \hat{i} - \frac{3}{2} m u \hat{i} - \frac{3}{2} m \hat{j} = 6 m v \Rightarrow - \frac{1}{2} m u \hat{i} - \frac{3}{2} m u \hat{j} = 6 m v \Rightarrow v = \frac{u}{12} (- \hat{i} - 3 \hat{j})$

Physics - Center of Mass Question with Solution | TestHub

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