Question Paper from: JEE Main 2021 - Paper 1

When a disc slides on a smooth inclined surface from rest, the time is taken to move from A to B is t1. When
the disc performs pure rolling from rest then the time taken to move from A to B is $t_{2}$ . If $\frac{t _{2}}{t _{1}} = \frac{3}{x}$ find x.

Correct Answer :

Solution:

Chapter Name: Rotational Motion

Difficulty Level: Difficulty

When the disc slides $a c c_{1} = g s in θ$

So $S = u t_{1} + \frac{1}{2} a c c_{1} t_{1}^{2} = \frac{1}{2} g s in θ . t_{1}^{2}$

When Disc do pure rolling $a c c_{2} = \frac{g s in θ}{1 + \frac{K ^{2}}{R ^{2}}} = \frac{g s in θ}{1 + \frac{1}{2}} = \frac{2}{3} s in θ$

So $S = u t_{2} + \frac{1}{2} . a c c_{2} . t_{2}^{2} = \frac{1}{2} . \frac{2}{3} g s in θ . t_{2}^{2}$

From (1) & (2)

$\frac{t _{2}}{t _{1}} = \frac{3}{2}$

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JEE Main 2021 - Paper 1

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