Question

A solid sphere is in pure rolling motion on an inclined surface having inclination $ \theta $ . Then:
(1) friction will increase its angular velocity and decrease its linear velocity
(2) if $ \theta $ decreases, friction will decrease
(3) frictional force acting on sphere is $ f=\mu \,mg\cos \theta $
(4) $ f $ is dissipative force

• A. 1 and 2 are correct
• B. 2 and 3 are correct
• C. 1 and 4 are correct
• D. 1, 2 and 3 are correct

Answer 1

Answer: (A)

In case of pure rolling,
$f=\frac{\frac{m g \sin \theta}{1+m R^{2}}{1}}{}$ (upwards)
$\therefore f \propto \sin \theta$
Therefore, as $\theta$ decreases force of friction will decrease.
Also due to friction its linear velocity decreases and angular velocity increases.