JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Laws of Motion

When a body slides down from rest along a smooth inclined plane making an angle of

3 0^{\circ}

with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time

α T

, where

α

is a constant greater than 1. The co-efficient of friction between the body and the rough plane is

\frac{1}{x} (\frac{α ^{2} - 1}{α ^{2}})

where

x =

______.

Answer: 3

Solution

On the smooth incline the acceleration is

a_{1} = g sin 3 0^{\circ}

and the distance from rest is

s = \frac{1}{2} a_{1} T^{2}

. On the rough incline

a_{2} = g sin 3 0^{\circ} - μg cos 3 0^{\circ}

and

s = \frac{1}{2} a_{2} (α T)^{2}

. Equal distances require

a_{1} = α^{2} a_{2}

, so

g sin 3 0^{\circ} = α^{2} (g sin 3 0^{\circ} - μg cos 3 0^{\circ})

. With

sin 3 0^{\circ} = \frac{1}{2}

and

cos 3 0^{\circ} = \frac{3}{2}

, this rearranges to

μ = \frac{1}{3} (\frac{α ^{2} - 1}{α ^{2}})

, so

x = 3

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Numerical answer

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JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Laws of Motion

Solution

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