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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. |
Answer» (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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