Question

Pendulum beating second at the equator ( g= 978 cm / sec${}^2$) is taken to Antarctica (g=983cm /sec${}^2$), Its length is not be increased by

• A. 0.1 cm
• B. 0.2 cm
• C. 0.4 cm
• D. 0.5 cm

Answer 1

The correct option is D 0.5 cm

The equation for the pendulum of time period is:

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

When g changes let the length of pendulum is l^’. Then,

$T=2\pi \sqrt{\frac{l}{g}}...\left(1\right)$

$T=2\pi \sqrt{\frac{l^{\prime }}{g^{\prime }}}...........\left(2\right)$

From equation (1) and (2)

$\frac{l}{g}=\frac{l^{\prime }}{g^{\prime }}$

$l^{\prime }=\frac{g^{\prime }}{g}l$

The change in length of pendulum is

$\Delta l=l^{\prime }-l$

$\Delta l=\frac{g^{\prime }}{g}l-l$

$\Delta l=\left(\frac{g^{\prime }-g}{g}\right)l$

$\Delta l=\left(\frac{g^{\prime }-g}{g}\right){\left(\frac{2}{2\pi }\right)}^{2}g$

$\Delta l=\frac{983-978}{10}$

$\Delta l=\frac{5}{10}$

$\Delta l=0.5cm$