Question

A seconds pendulum is taken to a place where acceleration due to gravity falls to one-fourth. How is the time period of the pendulum affected, if at all ? Give reason. What will be its new time period ?

Answer 1

Time period will be doubled

Time period with acceleration due to gravity g

$T_1=2\pi \sqrt{\frac{l}{g}}$

for a second's pendulum time period is 2s

when acceleration is one -fourth

$T_2=2\pi \sqrt{\frac{l}{\frac{g}{4}}}=2\times 2\pi \sqrt{\frac{l}{g}}=2\times T_1=4\times 2=4s$