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Q.

Two planets have the same mass, M. Each planet has a constant density, but the density of planet 2 is twice as high as that of planet 1 . Identical objects of mass m are placed on the surfaces of the planets. What is the relationship of the gravitational potential energy, U1 on planet 1 to U2 on planet 2 ?

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a

U1=2U2

b

U1=8U2

c

U1=21/3U2

d

U1=U2(2)1/3

answer is D.

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Detailed Solution

M=4π3R3ρ⇒R3ρ=cons⁡tan⁡t….(i)∵   U=−GMmr… (ii) from (i) and (ii), U∝ρ1/3.
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