Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth,
Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weigh
(a) W
(b) 2W
(c) W/2
(d) 21/3W at the planet.
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(d) 21/3 W at the planet.
EXPLANATION:
Since the density is same the volume and hence the radius of the planet will be more than the radius of the earth. Let the radius of the earth be R and that of the planet be R'. If the density is ρ, then
4πR'³ρ/3 = 2*4πR³ρ/3
→R'³ =2R³
→R' = 2¹/³R
Acceleration due to gravity on this planet = G*2M/R'² (M is mass of the earth)
=2GM/(2¹/³R)²
=2⁽¹⁻²/³⁾(GM/R²)
=2¹/³g
Hence the weight on the planet =2¹/³*mg =2¹/³W.
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