A ball P collides with another identical ball | vedclass

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(A) Let the mass of both balls be $m$. Let the initial velocity of ball $P$ be $u_1$ and ball $Q$ be $u_2 = 0$.After collision,let the velocities be $

Vedclass · Accepted Answer

$1/3$

Vedclass · Answer

(A) Let the mass of both balls be $m$. Let the initial velocity of ball $P$ be $u_1$ and ball $Q$ be $u_2 = 0$.After collision,let the velocities be $v_1$ and $v_2$ respectively.For a one-dimensional elastic collision between two identical masses where one is initially at rest,the final velocities are given by:$v_1 = \left(\frac{1-e}{2}\right) u_1$$v_2 = \left(\frac{1+e}{2}\right) u_1$Given that the velocity of ball $Q$ is twice the velocity of ball $P$ after collision,we have $v_2 = 2v_1$.Substituting the expressions:$\left(\frac{1+e}{2}\right) u_1 = 2 \left(\frac{1-e}{2}\right) u_1$$1 + e = 2(1 - e)$$1 + e = 2 - 2e$$3e = 1$$e = 1/3$

$A$ ball $P$ collides with another identical ball $Q$ at rest. For what value of coefficient of restitution $e$,will the velocity of ball $Q$ become two times that of ball $P$ after collision?

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