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Q.

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at 45° and the block is released from rest. The block takes a time t in moving a distance d. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time t/2 in moving down the same distance d. The coefficient of friction is

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a

3/4

b

5/4

c

1/2

d

1/2

answer is A.

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Detailed Solution

If the same wedge is made rough, then time taken by it to come down becomes n times more.For rough surface,    t=2sgsinθ-μgcosθ             ........(i)For smooth surface,  tn=2sgsinθ       ......(ii)Squaring Eqs. (i) and (ii) and dividing them, we getμ=1-1n2tanθ∴  μ=1-1n2tanθ=1-122tan45°⇒  μ=4-14=34
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To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at 45° and the block is released from rest. The block takes a time t in moving a distance d. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time t/2 in moving down the same distance d. The coefficient of friction is