A disc of radius 20, cm and mass half kg is rolling on an inclined plane. Find out friction force so

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6.System of Particles and Rotational Motion

hard

A disc of radius $20\, cm$ and mass half $kg$ is rolling on an inclined plane. Find out friction force so that disc performs pure rolling.

$\frac{5 \sqrt{2}}{3} N$

$\frac{5}{3 \sqrt{2}} N$

$\frac{5}{\sqrt{2}} N$

$\frac{5}{2 \sqrt{3}} N$

(AIIMS-2019)

Solution

Consider the following figure.

From the above figure,

$Mg \sin \theta- f = ma _{ cm }$

As we know that,

$\tau_{ cm }= I _{ cm } \alpha$

And,

$f =\frac{ MR ^{2}}{2}\left(\frac{ a _{ cm }}{ R ^{2}}\right)$

$=\frac{ Ma _{ cm }}{2}$

$a_{c m}=\frac{2 f_{R}}{M}$

Therefore,

$mg \sin \theta- f = M \left(\frac{2 f }{ M }\right)$

$f =\frac{ mg \sin \theta}{3}$

Substitute the values.

$f =\frac{1}{2}\left(\frac{10}{3}\right)\left(\frac{1}{\sqrt{2}}\right)$

$=\frac{5}{3 \sqrt{2}} N$

Standard 11

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A disc of radius $20\, cm$ and mass half $kg$ is rolling on an inclined plane. Find out friction force so that disc performs pure rolling.

Solution

Similar Questions

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