JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Conservation of Momentum

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If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be :

(A) $100%$ ✓ Correct
(B) $200%$
(C) $400%$
(D) $300%$

Answer: (A)

Solution

Momentum and kinetic energy are linked by

K = \frac{p ^{2}}{2 m}

, so

p = 2 m K

and

p \propto K

. Quadrupling the kinetic energy therefore doubles the momentum,

p_{f} = 2 p_{i}

, and

\frac{p _{f} - p _{i}}{p _{i}} \times 100 = \frac{2 p _{i} - p _{i}}{p _{i}} \times 100

The momentum increases by

100%

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option

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