A sphere P of mass m moving with velocity v u | vedclass

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(C) For a perfectly elastic collision between two identical masses where one is initially at rest,the conservation of linear momentum and kinetic ener

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(C) For a perfectly elastic collision between two identical masses where one is initially at rest,the conservation of linear momentum and kinetic energy leads to the following equations:$1$. Conservation of linear momentum: $m\vec{v} = m\vec{v}_P + m\vec{v}_Q$,which simplifies to $\vec{v} = \vec{v}_P + \vec{v}_Q$.$2$. Conservation of kinetic energy: $\frac{1}{2}mv^2 = \frac{1}{2}mv_P^2 + \frac{1}{2}mv_Q^2$,which simplifies to $v^2 = v_P^2 + v_Q^2$.From the momentum equation,we can write $v^2 = |\vec{v}_P + \vec{v}_Q|^2 = v_P^2 + v_Q^2 + 2v_P v_Q \cos 	heta$.Comparing this with the kinetic energy equation $v^2 = v_P^2 + v_Q^2$,we get $2v_P v_Q \cos 	heta = 0$.Since $v_P$ and $v_Q$ are non-zero,we must have $\cos 	heta = 0$,which implies $	heta = 90^o$.

$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$.

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