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Laws of Motion question

2012 · Q106
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Laws of Motion question

2012 · Q106

NEETPhysicsLaws of MotionMCQ+4 / −1
A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by
  1. A
    68%
  2. B
    41%
  3. C
    200%
  4. D
    100%
View written solutionFree

Correct answer: B

When a stone is dropped from a height h, it hits the ground with a momentum

P=m2ghP = m\sqrt {2gh} P=m2gh​     ....(1)

where m is the mass of the stone.
When the same stone is dropped from a height 2h (i.e. 100% of initial), then its momentum with which it hits the ground becomes

P′=m2g(2h)=2PP' = m\sqrt {2g\left( {2h} \right)} = \sqrt 2 PP′=m2g(2h)​=2​P     [Using (1)]     ...(2)

% change in momentum = P′−PP×100%{{P' - P} \over P} \times 100\% PP′−P​×100%

=2P−PP×100%=41%= {{\sqrt 2 P - P} \over P} \times 100\% = 41\%=P2​P−P​×100%=41%

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