Solve the following :


A solid sphere of mass $0.50 \mathrm{~kg}$ is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is $2 / 7$. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?


$F-f f=m a$

$\tau=I \alpha$

$(F R+f f R)=\left(\frac{2}{5} m R^{2}\right)\left(\frac{a}{R}\right)$

$F+f f=\frac{2}{5} m a$

$f f=\mu \mathrm{ii})$

Solving (i),(ii) and (iii)

$\mathrm{F}=3.3 \mathrm{~N}$

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