Question

The length of the second’s pendulum on the surface of earth is 1m. The length of second’s pendulum on the surface of moon, where g is $\frac{1}{6}th$ value of earth surface, is:

• A. $\frac{1}{6}m$
• B. $6m$
• C. $\frac{1}{36}m$
• D. $36m$

Answer 1

The correct option is A

$\frac{1}{6}m$

Case - 1
$T=2\pi \sqrt{\frac{\ell }{g}}$ ....(1)
$2=2\pi \sqrt{\frac{\ell }{g}}$
Case - 2
$T^{\prime }=2=2\pi \sqrt{\frac{{\ell }^{\prime }}{\frac{g}{6}}}$ ....(2)
From (1) and (2)
${\ell }^{\prime }=\frac{1}{6}m$