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>> $If effective length of a simple pendulum$

Question

If effective length of a simple pendulum is equal to radius of earth (R), time period will be

A

$T = π \frac{R}{g}$

B

$T = 2 π \frac{2 R}{g}$

C

$T = 2 π \frac{R}{g}$

D

$T = 2 π \frac{R}{2 g}$

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Solution

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Correct option is D)

formula,

$T = 2 π \frac{L R}{g ( R + L )}$

If the effective length of a simple pendulum is equal to the radius of the earth (R),

then,

$T = 2 π \frac{R \times R}{g ( R + R )}$

$= 2 π \frac{R ^{2}}{g ( 2 R )}$

$∴ T = 2 π \frac{R}{2 g}$

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