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A horizontal force F is applied through the center of mass of a solid sphere of mass m and radius R which lies on a horizontal rough surface. If the sphere rolls without slipping, the acceleration of the center of mass of the sphere will be (g = 10m/s²)

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$\frac{3 F}{5 M}$

F/M

$\frac{2 F}{3 M}$

$\frac{5 F}{7 M}$

answer is C.

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Detailed Solution

F – f = ma_cm .....(i)

$Rf = I_{cm} α$

$Rf = \frac{2}{5} {mR}^{2} (\frac{a}{R})$

$f = \frac{2}{5} m a . . . (ii)$

$F = \frac{2}{5} ma + ma$

$F = \frac{7}{5} ma \Rightarrow a = \frac{5}{7} \frac{F}{m}$

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