Question 703: Centre of Mass and Rotational Motion

Question

A solid sphere having mass $$m$$ and radius $$R$$ moves down a plane inclined at an angle '$$	heta$$'. Find the ratio between its acceleration when it rolls without slipping and its acceleration when it slides down the same plane without any rotation.

Accepted Answer

For solid sphere rolling without slipping on inclined plane, acceleration is given as,
$$a_1=\frac{g \sin 	heta}{1+k^2 / R^2}$$
For solid sphere slipping on inclined plane without rolling, acceleration is as follows.
$$a_2=g \sin 	heta$$
Therefore, required ratio $$=a_1 / a_2$$
$$=\frac{1}{1+\frac{k^2}{R^2}}=\frac{1}{1+\frac{2}{5}}=\frac{5}{7}$$

Answer

5 : 7

Answer

2 : 3

Answer

2 : 5

Answer

7 : 5

Centre of Mass and Rotational Motion

A solid sphere having mass $m and radius R moves down a plane inclined at an angle '\theta$'. Find the ratio between its acceleration when it rolls without slipping and its acceleration when it slides down the same plane without any rotation.

Choose the correct answer: