Question

A solid sphere of mass m is situated on a horizontal surface and a tangential force acts at the top of the sphere. If the sphere rolls without slipping then the acceleration of the center of the sphere would be?

• A. $\frac{5}{3}\frac{F}{m}$
• B. $\frac{3F}{5m}$
• C. $\frac{10F}{7m}$
• D. $\frac{7F}{10m}$

Answer 1

The correct option is C $\frac{10F}{7m}$

$\begin{array}{c}\text{let the Radius of the sphere be}R\\ \Rightarrow \text{Moment of Inertia of Sphere}I=\frac{2M{R}^2}{5}\\ \text{From translatory motion equation -}\\ F-f=ma-0\\ \text{From Rotatory motion equation-}\end{array}$

$\begin{array}{c}(F+f)R=I\alpha =\frac{2}{5}m{R}^2\alpha \\ \left(\text{Torgue}\right)\\ \Rightarrow F+f=\frac{2}{5}mR\alpha =\frac{2}{5}ma-\left(2\%\right(a=Ra)\text{Rotatory motion}\\ \text{From eq}D\text{and}\left(2\right)\text{we get}\\ 2F=\frac{7}{5}ma\Rightarrow a=\frac{10F}{7m}\end{array}$