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A sphere P of mass m, travelling with speed $u$, makes a head-on collision with a stationary sphere Q also of mass m. After the collision, the velocities of P and Q are $v_1$ and $v_2$ respectively. Which one of the followings is a possible pair values for $v_1$ and $v_2$?

A. $-u, 2u$

B. $u/4, 3u/4$

C. $3u/4, u/4$

D. $u/\sqrt2, u/\sqrt2$

Using conservation of momentum, I know $v_1 + v_2 = u$.

Using energy, I know $u^2 + v^2 \le u^2$.

So I not sure which one, B or C, is the answer.

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closed as too localized by Waffle's Crazy Peanut, dmckee May 26 '13 at 14:11

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You have clearly got a typo in the relation you give as arising from the conservation of energy. –  dmckee May 26 '13 at 14:10
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Some guidance on asking homework-like questions on Physics.SE. –  dmckee May 26 '13 at 14:12
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1 Answer 1

As the collision is not known to be elastic or inelastic. We just go with checking options , as you did. a),d) are easily eliminated . But now b),c) gives in problem.

Now we see that after collision the bodies must separate out. $$0\le\text{coefficient of restitution }(e)\le1 $$

Otherwise $e$ will go negative.

Now we can see in c) $e=-1/2$ but in b) : $e=1/2$. So, c is wrong.

> All velocities assumed to be in initial direction of motion of P

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