If the radius of the earth were increased by a factor of 2 keeping the mass constant by what factor would its density have to be changed to keep g the same?

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Solution

The correct option is C

$g = \frac{G M}{R^{2}} = \frac{G (\frac{4}{3} π R^{3} ρ)}{R^{2}} = \frac{4}{3} π G ρ R i . e ., g \propto ρ R$

R is increased by a factor of 2 i.e., to keep the value of g to be constant the value of $ρ$ has to be changed by a factor of $\frac{1}{2} .$

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If the radius of the earth were increased by a factor of 2 keeping the mass constant by what factor would its density have to be changed to keep g the same?

The correct option is C g=GMR2=G(43πR3ρ)R2=43πGρRi.e.,g∝ρR R is increased by a factor of 2 i.e., to keep the value of g to be constant the value of ρ has to be changed by a factor of 12.

The correct option is C

$g = \frac{G M}{R^{2}} = \frac{G (\frac{4}{3} π R^{3} ρ)}{R^{2}} = \frac{4}{3} π G ρ R i . e ., g \propto ρ R$

R is increased by a factor of 2 i.e., to keep the value of g to be constant the value of $ρ$ has to be changed by a factor of $\frac{1}{2} .$