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प्रश्न
A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find the length of a second pendulum at a place where g = π2 m/s2.
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उत्तर
It is given that:
Time period of the second pendulum, T = 2 s
Acceleration due to gravity of a given place, g =\[\pi^2\]ms−2
The relation between time period and acceleration due to gravity is given by,
\[\Rightarrow 2 = 2\pi\sqrt{\left( \frac{l}{\pi^2} \right)}\]
\[ \Rightarrow \frac{1}{\pi} = \frac{\sqrt{l}}{\pi}\]
\[ \Rightarrow l = 1 m\]
Hence, the length of the pendulum is 1 m.
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