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Question

Two bodies of masses 1 kg and 2 kg are projected with same velocities, on two rough surfaces whose coefficients of friction are 0.2 and 0.4 respectively. Find the ratio of distances travelled by them before their velocities become half of the initial value.

A
1:3
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B
2:1
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C
1:4
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D
4:1
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Solution

The correct option is B 2:1
The magnitude of a=fkm=μkmgm=μg
Initial velocity=u, Final velocity=v=u2,
Friction opposes motion, so a=μg,
Hence,
v2u2=2as; (u2)2u2=2μgs
s=3u28μg
Hence ratio of distance travelled by both bodies is inversely proportional to coefficient of friction.
s1s2=μ2μ1=2

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