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Question

# Two hailstones with radii in the ratio of 1 : 2 fall from a great height through the atmosphere. Then the ratio of their momentum after they have attained terminal velocity is

A
1 : 1
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B
1 : 4
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C
1 : 16
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D
1 : 32
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Solution

## The correct option is D 1 : 32p=mvwhere p=momentumm=massv=velocitym∝r3Here r=radiusNow v=29r2g(d2−d1)nwherer=radius of oil dropg=acceleration due to gravityd1=density of bodyd2=density of mediumSo v∝r2Asp=mv and m∝r3, v∝r2Therefore p∝r5Hence p1p2=(r1)5(r2)5Now r2=2r1So p1p2=(r1)5(2r1)5p1p2=132Hence the correct option is (D).

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