Question

A force of 49 N acts tangentially at the highest point of a sphere (solid sphere of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is :-

(1) \(2.5\ m/s^2\)

(2) \(3.5 \ m/s^2\)

(3) \(0.35\ m/s^2\)

(4) \(0.45\ m/s^2\)

Answer 1

Correct option is : (2) \(3.5 \ m/s^2\) 

F + f = ma

\((f - f)R = \frac{2}{5} mR^2 \frac{a}{R}\)

\(2F = \frac{7}{5}ma\)

\(a = \frac{10}{7} \times \frac{f}{m} = \frac{10}{7} \times \frac{49}{20} = 3.5\ m/s^2 \)