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=constant….(i)∵ U=−GMmr… (ii) from (i) and (ii), U∝ρ1/3.