Question

Two identical metallic blocks resting on a frictionless horizontal surface are connected by a light metallic spring having the spring constant $100\text{N/m}$ and an unstretched length of $0.2\text{m}$, as shown in figure 1. A total charge $Q$ is slowly placed on the system, causing the spring to stretch to an equilibrium length of $0.3\text{m}$, as shown in figure 2. The value of charge $Q$, assuming that all the charge resides on the blocks and that the blocks are like point charges , is

• A. $10\mu C$
• B. $15\mu C$
• C. $20\mu C$
• D. $30\mu C$

Answer 1

The correct option is C $20\mu C$

As masses are identical so net charge on each mass is $\frac{Q}{2}.$
Here electrostatic force must be balanced by spring force.
$F_e=\frac{1}{4\pi {ϵ}_0}.\frac{\left(Q/2\right)\left(Q/2\right)}{(0.3m{)}^2}=\left(100\text{N/m}\right)\left(0.1\text{m}\right)$
$Q^2=\frac{4\times 100\times \left(0.1\right)\times (0.3{)}^2}{9\times {10}^9}$
$\Rightarrow Q=20\times {10}^{-6}C=20\mu C$