Gravitation 5 Question 2

2. The mass and the diameter of a planet are three times the respective values for the earth. The period of oscillation of a simple pendulum on the earth is 2s. The period of oscillation of the same pendulum on the planet would be

(a) 23s

(b) 32s

(c) 23s

(d) 32s

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Answer:

Correct Answer: 2. (c)

Solution:

  1. Period of motion of a pendulum is given by

T=2πlg

On the surface of earth, let period of motion is Te and acceleration due to gravity is ge

Te=2πlge

On the another planet, let period of motion is Tp and gravitational acceleration is gp

Tp=2πlgp

( Pendulum is same, so l will be same)

From Eqs. (ii) and (iii),

TeTp=2πlge2πlgp=gpge

Now,

ge=GMeRe2 and gp=GMpRp2

Given, Mp=3Me and Rp=3Re

gp=G×3Me9Re2=13GMeRe2=13gegpge=13 or gpge=13

From Eqs. (iv) and (v), Tp=3Te

or

Tp=23s

(Te=2s)



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