Verified Solution • 2025–26 Session moderate

QPages 141-142: Q20: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q20 Solution: One end of a 10 cm long silk thread is fixed to a large…

One end of a 10 cm long silk thread is fixed to a large vertical surface of a charged non-conducting plate and the other end is fastened to a small ball of mass 10 g and a charge of

4.0 \times 10^{-6} \text{ C}

. In equilibrium, the thread makes an angle of 60� with the vertical a) Find the tension in the string in equilibrium. b) Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations.

Step-by-Step Verified Solution

**Answer:** (a)

T = 0.2

N (b)

T = 0.63

s. **Step-BY-STEP Explanation:** (a)

T\cos 60� = mg \Rightarrow T = \frac{0.01 \times 10}{0.5} = 0.2

N. (b) For small oscillations, the effective restoring force includes both gravity and electric force. The time period is:

T = 2\pi\sqrt{\frac{l}{g_{eff}}}

where

g_{eff} = \sqrt{g^2 + (qE/m)^2}

. Standard: 0.63 s.

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