A ball of mass m is moving with a speed V as | vedclass

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(D) The collision occurs along the line joining the centers of the two balls. The angle between the velocity vector $V$ and the line of impact is $30^

Vedclass · Accepted Answer

$\frac{\sqrt{3}V}{4}$

Vedclass · Answer

(D) The collision occurs along the line joining the centers of the two balls. The angle between the velocity vector $V$ and the line of impact is $30^{\circ}$.The component of velocity along the line of impact is $u = V \cos 30^{\circ} = \frac{\sqrt{3}V}{2}$.Let $v_1$ be the velocity of the ball of mass $2m$ and $v_2$ be the velocity of the ball of mass $m$ along the line of impact after the collision.Applying the law of conservation of linear momentum along the line of impact:$m u = m v_2 + (2m) v_1$$u = v_2 + 2v_1$  --- $(1)$Applying the coefficient of restitution formula $(e = 1/2)$:$e = \frac{v_1 - v_2}{u}$$\frac{1}{2} = \frac{v_1 - v_2}{u}$$u = 2v_1 - 2v_2$ --- $(2)$Adding equations $(1)$ and $(2)$:$2u = 4v_1 - v_2 + v_2 = 4v_1$$v_1 = \frac{u}{2} = \frac{\sqrt{3}V}{2 	imes 2} = \frac{\sqrt{3}V}{4}$.

$A$ ball of mass $m$ is moving with a speed $V$ as shown in the figure. It undergoes an inelastic collision with a ball of mass $2m$ which was initially at rest. The velocity of the ball of mass $2m$ after the collision is given by

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