Consider a planet in some solar system which has a mass double the mas

1.	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 Won the earth will weigh(a) W(b) 2 W(c) W/2(d) 21/3 W at the planet.
Answer» (d) 2^1/3 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 = 24πR³ρ/3 →R'³ =2R³ →R' = 2¹/³R Acceleration due to gravity on this planet = G2M/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.

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 Won the earth will weigh(a) W(b) 2 W(c) W/2(d) 21/3 W at the planet.

Answer»

(d) 2^1/3 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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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 Won the earth will weigh(a) W(b) 2 W(c) W/2(d) 21/3 W at the planet.

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