If P is the momentum of a particle and K is the kinetic energy of a particle then which of the following is correct statement:
I) If P is increased by 200% corresponding change in K is 200%
II) If K is increased by 300% corresponding change in P is 800%
III) If P is increased by 1% corresponding change in K is 2%
IV) If K is increased by 1% corresponding change in P is 0.5%

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III, IV

I, III, IV

I, II, III, IV

II, III, IV

answer is A.

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Detailed Solution

A) $K = \frac{p^{2}}{2 m}$

$K' = \frac{{(3 p)}^{2}}{2 m} = 9 (\frac{p^{2}}{2 m}) = 9 K$

$∴ %$ increase in $K = 800 %$

B)    $P = \sqrt{2 k m}$
   $P' = \sqrt{2 (4 K) m} = 2 \sqrt{2 k m} = 2 P$
$∴ %$ increase in $P = 100 %$
C) $K = \frac{P^{2}}{2 m}$
For small percentage changes,
% increase in $K = 2$ (% increase in P) $= 2 %$
D) $P = \sqrt{2 k m} = {(2 k m)}^{1 / 2}$
% increase in $P = \frac{1}{2}$ (% increase in K) $0.5 %$