Centre of Mass 3 Question 11
14. This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
(2013 Main)
Statement I A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as $f \frac{1}{2} m v^{2}$, then
$f=\frac{m}{M+m}$.
Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision.
(a) Statement I is true, Statement II is true, and Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is true, but Statement II is not the correct explanation of Statement I
(c) Statement I is true, Statement II is false
(d) Statement I is false, Statement II is true
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Answer:
Correct Answer: 14. (d)
Solution:
- Maximum energy loss
$$ =\frac{p^{2}}{2 m}-\frac{p^{2}}{2(m+M)} \quad \because KE=\frac{p^{2}}{2 m} $$
Before collision the mass $m$ and after collision the mass is $m+M$
$$ =\frac{p^{2}}{2 m} \frac{M}{(m+M)}=\frac{1}{2} m v^{2} \quad \frac{M}{m+M} \quad f=\frac{M}{m+M} $$
