A planet has double the mass of the Earth. Its average density is equal to that of the Earth. An object weighing W on Earth will weigh on that planet [2023]

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Solution

Q.
A planet has double the mass of the Earth. Its average density is equal to that of the Earth. An object weighing W on Earth will weigh on that planet [2023]

1 $2^{1 / 3} W$

2 $W$

3 $2^{2 / 3} W$

4 $2 W$

Ans.
(1)

$m = ρ \times \frac{4}{3} π R^{3}$

$R \propto m^{1 / 3} (ρ = constant)$

$Weight = W \propto g \propto \frac{G m}{R^{2}}$

$W \propto \frac{m}{m^{2 / 3}} \propto m^{1 / 3}$

$So, W' = {(2)}^{1 / 3} W$

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