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(A) Let the mass of each ball be $m$. Let the initial velocity of the first ball be $u$ and the second ball be $0$. Let the velocities after the colli

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(A) Let the mass of each ball be $m$. Let the initial velocity of the first ball be $u$ and the second ball be $0$. Let the velocities after the collision be $v_1$ and $v_2$ respectively. According to the problem,$v_2 = 2v_1$.By the Conservation of Linear Momentum $(COLM)$:$m(u) + m(0) = m(v_1) + m(v_2)$$u = v_1 + v_2$Since $v_2 = 2v_1$,we have $u = v_1 + 2v_1 = 3v_1$,which implies $v_1 = \frac{u}{3}$ and $v_2 = \frac{2u}{3}$.The coefficient of restitution $e$ is defined as:$e = \frac{v_2 - v_1}{u_1 - u_2}$Substituting the values:$e = \frac{2v_1 - v_1}{u - 0} = \frac{v_1}{u}$Since $v_1 = \frac{u}{3}$,we get:$e = \frac{u/3}{u} = \frac{1}{3}$

Ball $1$ collides with another identical ball at rest. For what value of coefficient of restitution $e,$ the velocity of the second ball becomes two times that of the first ball after the collision?

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