Question

The mass and diameter of a planet are twice those of the earth. The period of oscillation of a pendulum on this planet will be, if it is a seconds pendulum on the earth

• A. $2.4s$
• B. $2.8s$
• C. $3.2s$
• D. Infinity

Answer 1

Answer: (B)

$2.8s$

Seconds pendulumhas time period of 2 seconds.

$T_{earth}=2\pi \sqrt{\frac{l{R}^2}{GM}}$

$g=\frac{GM}{R^2}$
$T_{planets}=2\pi \sqrt{\frac{l\times 4R^2}{2GM}}=\sqrt{2}{T}_{earth}$
$=\sqrt{2}\times 2=2.8sec$