QJEEM21Ph60aa: JEE Main 2021 Physics - Class 11 JEEM21Ph60aa Solution: A solid disc of radius 'a' and mass 'm' rolls down without…

Question

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A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle

θ

with the horizontal. The acceleration of the disc will be

\frac{2}{b}

g sin

θ

where b is ____________. (Round off to the Nearest Integer) (g = acceleration due to gravity,

θ

= angle as shown in figure)

JEE Main 2021 (Online) 16th March Evening Shift Physics - Rotational Motion Question 109 English

Accepted Answer

We know that, on an inclined plane

Acceleration, $a = \frac{g \sin θ}{1 + \frac{I}{m R^{2}}}$

$\Rightarrow a = \frac{g \sin θ}{1 + \frac{1}{2}}$ [ $∵$ For disc, $I = \frac{m R^{2}}{2}$ ]

$\Rightarrow a = \frac{2}{3} g \sin θ$ ....... (i)

As per question, acceleration of the disc will be $\frac{2}{b} g \sin θ$ .

Comparing it with Eq. (i), we get

$b = 3$

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