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Pendulum beating seconds at the equator (g = 978 cm / sec²) is taken to Antarctica (g=983 cm/sec²). If initial length is 100cm its length is to be increased by

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By Expert Faculty of Sri Chaitanya

a

0.1 cm

b

0.2 cm

c

0.4 cm

d

0.5 cm

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detailed solution

Correct option is D

$\begin{array}{l} T = 2 π \sqrt{\frac{ℓ}{g}}; ℓ_{1} = 100 cm (seconds pendulum) \\ \frac{ℓ_{2}}{ℓ_{1}} = \frac{g_{2}}{g_{1}} = \frac{983}{978} \Rightarrow \frac{ℓ_{2} - ℓ_{1}}{ℓ_{1}} = \frac{983}{978} - 1 = \frac{983 - 978}{978} \\ ℓ_{2} - ℓ_{1} = 100 \times \frac{983 - 978}{978} = 0 .5 cm \end{array}$

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