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QPages 121-124: Q50: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q50 Solution: The bob of a simple pendulum has a mass of 40 g and a positive…

The bob of a simple pendulum has a mass of 40 g and a positive charge of 4.0×10−6 C4.0 \times 10^{-6} \text{ C}. It makes 20 oscillations in 45 s. A vertical electric field pointing upward and of magnitude 2.5×104 N C−12.5 \times 10^4 \text{ N C}^{-1} is switched on. How much time will it now take to complete 20 oscillations?

Step-by-Step Verified Solution

**Answer:** t=45t = 45 s. **Step-BY-STEP Explanation:** Initially: 20 oscillations in 45 s, so T=2.25T = 2.25 s. T=2πl/g⇒l=gT24π2=1.29T = 2\pi\sqrt{l/g} \Rightarrow l = \frac{gT^2}{4\pi^2} = 1.29 m. With electric field: effective gravity g′=g−qEm=10−4×10−6×2.5×1040.04=10−2.5=7.5g' = g - \frac{qE}{m} = 10 - \frac{4 \times 10^{-6} \times 2.5 \times 10^4}{0.04} = 10 - 2.5 = 7.5 m/s_.
T′=2πlg′=2.6 sT' = 2\pi\sqrt{\frac{l}{g'}} = 2.6 \text{ s}
Time for 20 oscillations = 20×2.6=5220 \times 2.6 = 52 s. Standard: 45 s .

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