Physics - Electrostatics Question with Solution | TestHub

Force on each charged hemisphere: $F=\sigma E_0\pi R^2$ along its axis, acting at its centroid $\frac{R}{2}$ from the centre; the two forces are equal and opposite, so the net force on the shell is zero.

Torque about the centre: $\tau =2\sigma \pi R^3{E}_0\sin 37^{\circ }=\frac{6}{5}\pi \sigma E_0{R}^3$.

Rolling: $f=m{a}_{cm}$, $a_{cm}=R\alpha$; $\tau =I_{cm}\alpha +fR=\frac{5}{3}m{R}^2\alpha$ ⇒ $\alpha =\frac{18}{25}\frac{\pi \sigma E_{0}R}{m}$.

$f=\frac{18}{25}\pi \sigma E_0{R}^2$ - (B); $a_{cm}=\frac{18}{25}\frac{\pi \sigma E_0{R}^2}{m}$, not $\frac{12}{25}$ - (C), (D) wrong.

Topmost point: $a=a_{cm}+R\alpha =\frac{36}{25}\frac{\pi \sigma E_0{R}^2}{m}$ - (A)