Gravitation - Result Question 18

18. Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g, then

(a) g=g/9

(b) g=27g

(c) g=9g

(d) g=3g

[2005]

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Answer:

Correct Answer: 18. (d)

Solution:

  1. (d) We know that

g=GMR2=G(43πR3)ρR2=43πGRρ

g depends on radius of the planet

gg=RR=3RR=3[ As G & ρ are constants]

g=3g

If the radius of a planet decreases by n, keeping its mass unchanged, the acceleration due to gravity on its surface increases by 2n

Δgg=2ΔRR=2(n)=2n



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