Question

The length of seconds pendulum is 1 m on earth. If mass and diameter of the planner is double than that of earth,then length becomes

• A. 1 m
• B. 2 m
• C. 0.5 m
• D. 4 m

Answer 1

The correct option is C 0.5 m

$\begin{array}{c}{T}^{2}isproporetionalto\frac{l}{g},wherelisthelengthandgistheaccelerationduetogravity.\\ so\frac{l}{g}iscons\tan t.\\ g=\frac{GM}{R^2}\\ Massanddiameteraredoubled\\ So,g\cdot 1=\frac{g}{2}\\ =\frac{1}{g}-\frac{1}{\frac{g}{2}}\\ =\frac{1}{2}=0.5m\end{array}$

Hence,

option $\left(C\right)$ is correct answer.