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7.Gravitation
medium
A planet has double the mass of the earth. Its average density is equal to the that of the earth. An object weighing $W$ on earth will weigh on that planet:
A$2^{2 / 3} W$
B$W$
C$2^{1 / 3} W$
D$2 W$
(JEE MAIN-2023)
Solution
$m =\rho \times \frac{4}{3} \pi R ^3$
$R \propto m ^{\frac{1}{3}}(\rho=\text { constan } t)$3
$\text { weight }= W \propto g \propto \frac{ Gm }{ R ^2}$
$W \propto \frac{ m }{ m ^{2 / 3}} \propto m ^{1 / 3}$
$\text { So, } W ^1=(2)^{1 / 3}\,W$
$R \propto m ^{\frac{1}{3}}(\rho=\text { constan } t)$3
$\text { weight }= W \propto g \propto \frac{ Gm }{ R ^2}$
$W \propto \frac{ m }{ m ^{2 / 3}} \propto m ^{1 / 3}$
$\text { So, } W ^1=(2)^{1 / 3}\,W$
Standard 11
Physics
