Question #61455

1 Answer
Oct 19, 2016

(b) 13

Explanation:

As per Law of Universal Gravitation the force of attraction between two bodies is given as

FG=GM1.M2r2

Where G is gravitational constant.
It has the value 6.67408×1011m3kg1s2.
Comparing it with the expression
F(weight)=mg
we get value of g=GMer2e ......(1)
If ρ is density of earth, then
ρ=MeVolume
ρ=Me43πr3e
Me=43πρr3e
Inserting above value of mass of earth in (1) we get
g=G43πρr3er2e
g=G43πρre
gρre
From above we see that if radius of earth is increased by a factor of 3, to keep value of g same we need to decrease value of ρ by a factor of 3.
Hence we get 13