JEE Main · 2013 · 07 Apr 2013 · Offline · Conservation of Momentum

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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.
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, Statement - II is not a correct explanation of Statement - I.
(B)Statement - I is true, Statement - II is false.
(C)Statement - I is false, Statement - II is true✓ Correct
(D)Statement - I is true, Statement - II is true, Statement - II is a correct explanation of Statement - I.

Answer: (C)

Solution

The greatest possible energy loss happens when the two bodies stick and move off together, so Statement II is sound. To check the fraction, work in the centre-of-mass frame, where the kinetic energy available to be lost is

\frac{1}{2} \frac{m M}{M + m} v^{2}

. Comparing this with the incoming kinetic energy

\frac{1}{2} m v^{2}

, the fraction lost is

f = \frac{M}{M + m}

, not

\frac{m}{M + m}

as Statement I claims. Statement I is therefore false while Statement II is true.

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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JEE Main · 2013 · 07 Apr 2013 · Offline · Conservation of Momentum

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