(C) For a body rolling down an inclined plane without slipping,the condition for static friction is given by $\mu_s \geq \frac{\tan \theta}{1 + R^2/K^

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(C) For a body rolling down an inclined plane without slipping,the condition for static friction is given by $\mu_s \geq \frac{\tan \theta}{1 + R^2/K^2}$.For a solid cylinder,the radius of gyration $K$ is given by $K^2 = \frac{1}{2} R^2$,which implies $\frac{K^2}{R^2} = \frac{1}{2}$ or $\frac{R^2}{K^2} = 2$.Substituting this into the condition: $\mu_s \geq \frac{\tan \theta}{1 + 2}$.$\mu_s \geq \frac{\tan \theta}{3}$.Rearranging the terms,we get $\tan \theta \leq 3 \mu_s$.

Class 11 Physics System of Particles and Rotational Motion Rolling On Inclined Plane

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$A$ solid cylinder is rolling down on an inclined plane of angle $\theta$. The coefficient of static friction between the plane and the cylinder is $\mu_s$. The condition for the cylinder not to slip is

A
$\tan \theta \geq 3 \mu_s$
B
$\tan \theta > 3 \mu_s$
C
$\tan \theta \leq 3 \mu_s$
D
$\tan \theta < 3 \mu_s$

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System of Particles and Rotational Motion

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Rolling On Inclined Plane

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$A$ solid cylinder is rolling down on an inclined plane of angle $\theta$. The coefficient of static friction between the plane and the cylinder is $\mu_s$. The condition for the cylinder not to slip is

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