WBJEE · Physics · Oscillations
A simple pendulum is taken at a place where its distance from the earth's surface is equal to the radius of the earth. Calculate the time period of small oscillations if the length of the string is 4.0 m . (Take \(\mathrm{g}=\pi^2 \mathrm{~ms}^{-1}\) at the surface of the earth.)
- A 4 s
- B 6 s
- C 8 s
- D 2 s
Answer & Solution
Correct Answer
(C) 8 s
Step-by-step Solution
Detailed explanation
\(\mathrm{T}=2 \pi \sqrt{\ell / \mathrm{g}}, \quad \mathrm{g}_{\mathrm{h}=\mathrm{R}}=\frac{\mathrm{gR}^2}{\mathrm{r}^2}=\mathrm{g} / 4, \quad \mathrm{~T}=2 \pi \sqrt{\frac{4}{\pi^2 / 4}}=\frac{2 \pi \times 4}{\pi}=8 \mathrm{~m} / \mathrm{s}^2\)
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