Question

A seconds pendulum is shifted from a place where $g=9.8m/s^2$ to another place where $g=9.78m/s^2$. The change in its length so that its time period of oscillation does not change is

• A. Should be decreased by $\frac{2}{{\pi }^2}$ cm
• B. Should be increased by $\frac{2}{{\pi }^2}$ cm
• C. Should be increased by $\frac{2}{\pi }$cm
• D. Should be decreased by $\frac{2}{\pi }$cm

Answer 1

The correct option is A Should be decreased by $\frac{2}{{\pi }^2}$ cm

$T_1=2\pi \sqrt{\frac{l_1}{g_1}};T_2=2\pi \sqrt{\frac{l_2}{g_2}}$
Here
$\frac{l_1}{g_1}=\frac{l_2}{g_2}$
$\frac{l_2}{l_1}=\frac{g_2}{g_1}$
Thus length should decrease by the same percentage
as $g$ decreased. Thus it should decrease by $\frac{2}{{\pi }^2}cm$ from $1$ m.