First slide

Friction

Question

The lengths of smooth & rough inclined planes of $45^{0}$ inclination is same. Times of sliding of a body on two surfaces is $t_{1}, t_{2}$ and $μ$ = 0.5, then $t_{1} : t_{2} =$

Moderate

A

$\sqrt{2} : 1$
B

$2 : 3$
C

$1 : \sqrt{2}$
D

$3 : 2$

Solution

$\frac{t_{1}}{t_{2}} = \sqrt{\frac{2 l}{g \sin θ}} \sqrt{\frac{g (\sin θ - μ_{K} \cos θ)}{2 ℓ}}$
$= \sqrt{\frac{\sin θ - μ_{K} \cos θ}{\sin θ}} = \sqrt{1 - μ_{K} \cot θ}$

$= \sqrt{1 - 0.5} = \frac{1}{\sqrt{2}}$

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