Question

The shown system is in equilibrium. Suppose the ball is slightly pushed and released. The time period of small oscillations performed by the ball is

• A. $0.44\text{s}$
• B. $0.55\text{s}$
• C. $0.66\text{s}$
• D. $0.77\text{s}$

Answer 1

The correct option is A $0.44\text{s}$

FBD of the ball at equilibrium:


We know that, time period of a simple pendulum is, $T=2\pi \sqrt{\frac{l}{g_{eff}}}\dots \left(1\right)$
Here, $g_{eff}=\sqrt{g^2+{\left(\frac{qE}{m}\right)}^2}=\sqrt{g^2+{\left(\frac{q\sigma }{2{ϵ}_{0}m}\right)}^2}$
$g_{eff}=\sqrt{{10}^2+{\left(\frac{4\times {10}^{-6}\times 7.8\times {10}^{-7}}{2\times 9\times {10}^{-12}\times 10\times {10}^{-3}}\right)}^2}$
$g_{eff}=20{\text{m/s}}^2$
From (1),
$T=2\pi \sqrt{\frac{0.1}{20}}=0.44\text{s}$