Solveeit Logo

Question

Physics Question on Oscillations

The length of second's pendulum is 1m1\, m on earth. If mass and diameter of a planet is doubled than that of earth, then its length becomes:

A

1 m

B

2 m

C

0.5 m

D

4 m

Answer

0.5 m

Explanation

Solution

The acceleration due to gravity of earth is equal in magnitude to the force exerted by the earth on a body of unit mass. The motion of the bob is simple harmonic, hence its time period is given by T=2π displacement  acceleration T=2 \pi \sqrt{\frac{\text { displacement }}{\text { acceleration }}} =2πlg=2 \pi \sqrt{\frac{l}{g}} Also if the periodic time of a pendulum is 22 seconds, then it is called a second's pendulum. Also, g=GMR2g=\frac{G M}{R^{2}} where, MM is mass and RR is radius. T=2πR2lGM=2\therefore T=2 \pi \sqrt{\frac{R^{2} l}{G M}}=2 ...(i) Second's pendulum on other planet is 2=2π4R2lG(2M)2=2 \pi \sqrt{\frac{4 R^{2} l'}{G(2 M)}} ...(ii) From Eqs. (i) and (ii), we have R2lGM=4R2lG(2M)\frac{R^{2} l}{G M} =\frac{4 R^{2} l'}{G(2 M)} l=0.5m\Rightarrow l'=0.5\, m Hence, length of pendulum on planet is 0.5m0.5\, m.