Question

Mass of Pluto=1/2of mass of earth. Radius of Pluto=1/2of radius of earth. Find gp/ge.

Answer 1

g on earth (ge) = (Gm)/(R)²

where m = mass of earth

Given,

Pluto's mass = 1/2 of earth => m/2

Pluto's radius = 1/2 of earth => r/2

So g on pluto (gp) =
$\frac{capital \: g \times \frac{m}{2} }{( \frac{r}{2}) {}^{2} }$
(Here, capital g = G)

=> gp =
$capital \: g \: \times \frac{m}{2} \div (\frac{r}{2} ) {}^{2} \\ \\ = > capital \: g \: \times \frac{m}{2} \div \frac{ {r}^{2} }{4} \\ \\ = > capital \: g \frac{m}{2} \times \frac{4}{ {r}^{2} }$


=> gp = Gm/2 × 4/r²

=> gp = 4Gm/2r²

=> gp = 2Gm/r²

Now, ge = Gm/r²

and gp = 2Gm/r²

=> gp/ge = 2Gm/r² ÷ Gm/r²

=> gp/ge = 2Gm/r² × r²/Gm

(cancelling r² and Gm)

=> gp/ge = 2/1


Hope it helps dear friend ☺️✌️