A block of mass ' $\mathrm{m}$ ' and charge ' $\mathrm{q}$ ' is connected to a point ' $O$ ' with an…
A block of mass ' $\mathrm{m}$ ' and charge ' $\mathrm{q}$ ' is connected to a point ' $O$ ' with an inextensible string. This system is on a horizontal table. An electric field (E) is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field is
$\mathrm{qE}$
$2 \mathrm{qE}$
$\frac{3 \mathrm{qE}}{4}$
$3 \mathrm{qE}$
Solution
Let the length of the string is L Using the work energy theorem $F \cdot L=\frac{1}{2} m v^2-0$
$q E \cdot L=\frac{1}{2} m v^2 \Rightarrow v^2=\frac{2 q E L}{m}$
If $\mathrm{T}$ is the tension in the string.
When it becomes parallel to the electric field.
$\begin{aligned}
& T-q E=\frac{m v^2}{L} \\
& T=q E+\frac{m v^2}{L} \\
& =q E+\frac{m}{L} \times \frac{2 q E L}{M} ; T=3 q E
\end{aligned}$