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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

Asked in AIPMT 2011 Mains · Impulse and the change in momentum

Answer: (2) 41%

Step-by-step solution

Given: the height is increased by 100%, so the new height is 2h.

Idea: from rest, v=√2gh, so momentum P=m√2gh goes as √h.

(P₂)/(P₁)=√(2h)/h=√2.

√2=1.414.

Fractional change =√2-1=0.414.

That is an increase of about 41%.

Why the other options are wrong

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