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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

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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
Some guidance on asking homework-like questions on Physics.SE. – dmckee May 26 '13 at 14:12

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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