Question

In the figure below, $10\text{mC}$ charge is fixed. A $50\mu \text{C}$ charge having mass $10\text{g}$ is projected from infinity towards the $10\text{mC}$ charge. Calculate initial velocity of projection if minimum distance between the charges is $10\text{cm}$.

• A. $2000{\text{ms}}^{-1}$
• B. $3000{\text{ms}}^{-1}$
• C. $4000{\text{ms}}^{-1}$
• D. $5000{\text{ms}}^{-1}$

Answer 1

The correct option is B $3000{\text{ms}}^{-1}$

Using conservation of energy,
K.E at $\infty$ = P.E of system at minimum distance
$\frac{1}{2}m{v}_0^2=\frac{k{q}_1{q}_2}{r_{min}}$
$\Rightarrow \frac{1}{2}\times 10\times {10}^{-3}\times v_0^2=\frac{9\times {10}^9\times 10\times {10}^{-3}\times 50\times {10}^{-6}}{10\times {10}^{-2}}$
$\Rightarrow v_0^2=9\times {10}^6$
or $v_0=3000\text{m/s}$