Question

A wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of uniform vertical electric field $E$, as shown in the figure. The value of $E$ is -

• A. $\frac{mg}{2q}$
• B. $\frac{mg}{q}$
• C. $\frac{2mg}{q}$
• D. $\frac{3mg}{q}$

Answer 1

The correct option is A $\frac{mg}{2q}$


From the FBD,

$mg\sin \theta =f$

Where, $f=$ frictional force

Taking torque about centre of mass,

$fr\left(\text{clockwise}\right)=pE\sin \theta \left(\text{anti-clockwise}\right)$

Where, $r=$ radius of the wheel

$\left(mg\sin \theta \right)r=q\left(2r\right)E\sin \theta$

$\Rightarrow E=\frac{mg}{2q}$