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Q.26) There are two inclined surfaces of equal length $(L)$ and same angle of inclination $45^{\circ}$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smopth surface. The coefficient of kinetic friction $\left(\mu_k\right)$ between the object and the rough surface is close to

A) 0.75

B) 0.25

C) 0.40

D) 0.5

Answers (1)

best_answer

We know the time take for body to slide down incline is,

$t = \sqrt{\frac{2L}{g(\sin \theta - \mu_k \cos \theta)}}$

For smooth surface, $\mu_k = 0$

$t_\text{rough} =2 \times  t_\text{smooth}$
$\implies \frac{1}{1 - \mu_k} = 2 $
$\implies \mu_k = 0.5$

Hence, the answer is the option 4.

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Dimpy

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