Question

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at ${45}^o$ 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

• A. $3/4$
• B. $5/4$
• C. $1/2$
• D. $1/\sqrt{2}$

Answer 1

The correct option is A $3/4$

The acceleration of the block down the rough surface=$a_1=g(sin\theta -\mu cos\theta )$

The acceleration of the block down the smooth surface=$a_2=gsin\theta$

Distance traveled by object in time $T$ is given by

$D=\frac{1}{2}a{T}^2$
Hence $d=\frac{1}{2}{a}_1{t}_1^2=\frac{1}{2}{a}_2{t}_2^2$

$⟹\frac{a_1}{a_2}=1-\mu =\frac{t_2^2}{t_1^2}=\frac{1}{4}$

$⟹\mu =\frac{3}{4}$