Question

Pls answer
if acceleration due to gravity is one-fourth then how is time doubled.. if you only have the length of the simple pendulum...

Answer 1

$t = 2pi \sqrt{l \div g}$

Answer 2

You can observe this in formula for finding the time period if the pendulum.
$T_{1} = 2\pi \sqrt{ \frac{l}{g} }$
and when, g becomes ¼ of itself,
$T_{2} = 2\pi \sqrt{ \frac{4l}{g} } \\ \implies T_{2} = 2\pi \times 2 \sqrt{ \frac{l}{g} } \\ \implies T_{2} =2(2\pi \sqrt{ \frac{l}{g} } ) \\ \implies T_{2} =2(T_{1})$
Thus, if acceleration due to gravity is one-fourth then time is doubled.

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