A uniform solid sphere of mass m and radius R | vedclass

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(C) Let $m$ be the mass and $R$ be the radius of the solid sphere. The force $F$ is applied at the top point. $1$. Equation of linear motion: $F + f =

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$\frac{7}{10} ma$

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(C) Let $m$ be the mass and $R$ be the radius of the solid sphere. The force $F$ is applied at the top point. $1$. Equation of linear motion: $F + f = ma$,where $f$ is the friction force acting at the point of contact $A$ in the direction of motion. $2$. Equation of rotational motion about the center of mass: $F 	imes R - f 	imes R = I \alpha$,where $I = \frac{2}{5} mR^2$ is the moment of inertia and $\alpha = \frac{a}{R}$ is the angular acceleration. Substituting $I$ and $\alpha$: $F R - f R = (\frac{2}{5} mR^2) (\frac{a}{R}) \Rightarrow F - f = \frac{2}{5} ma$. $3$. Adding the two equations: $(F + f) + (F - f) = ma + \frac{2}{5} ma \Rightarrow 2F = \frac{7}{5} ma \Rightarrow F = \frac{7}{10} ma$.

$A$ uniform solid sphere of mass $m$ and radius $R$ is being pulled on a horizontal surface with a force $F$ parallel to the surface,applied at its topmost point. If the acceleration of the center of mass of the sphere is $a$ and it is rolling without slipping on the surface,the value of $F$ is:

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