Q89 / 180 · JIPMER 2015 · Physics

A tangential force acting on the top of sphere of mass $m$ kept on a rough horizontal place as shown in figure. Figure If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

  • Correct answer
    A
    $\frac{10 F}{7 \mathrm{~m}}$
  • B
    $\frac{F}{2 m}$
  • C
    $\frac{3 F}{7 m}$
  • D
    $\frac{7 F}{2 m}$

Solution

Let $a$ be the acceleration of centre of sphere. The angular acceleration about the centre of the sphere is $\alpha=\frac{a}{r}$, as there is no slipping. For the linear motion of the centre $f+F=m a$ ...(i) and for the rotational motion about the centre $F r-f r=I \alpha=\left(\frac{2}{5} m r^2\right)\left(\frac{a}{r}\right)$ $\Rightarrow \quad F-f=\frac{2}{5} m a$ ...(ii) From Eqs. (i) and (ii) $2 F=\frac{7}{5} m a \Rightarrow a=\frac{10 F}{7 m}$

Hence, the correct answer is option: 'A'.

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