SHMMedium
Question
Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum $L$, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as: (Take $\pi^{2} = 9.8$, and $g = 9.8\text{ }m/s^{2}$ )
Options
A.0.75 m
B.1.5 m
C.2 m
D.1 m
Solution
Sol. [Key Concept: Simple-pendulum experiment: effective length] Time taken for 30 oscillations $= 60\text{ }s$
Time period of simple pendulum = Time taken for 1 oscillation
$$\begin{matrix} & \ \Rightarrow T = \frac{60}{30} = 2\text{ }s \\ & T = 2\pi\sqrt{\frac{I}{g}} \Rightarrow I = \frac{gT^{2}}{4\pi^{2}} = \frac{9.8 \times 2 \times 2}{4 \times 9.8} = 1\text{ }m \end{matrix}$$
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