Question

The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio [MH CET 2004]
A) 1 : 2 B) 2 : 1 C) 3 : 5 D) 5 : 3

Answer 1

Acc to law of gravitation : mg1=GM1m/R1^2
g1= GM1 / R1^2
( considering that for the first planet variables are placed with 1 and for the second with 2 )
Similarly g2 = G M2/R2^2
As we know that M2 is twice of M1 and R2 is twice of R1
So g2= G2M1/(2R1)^2
g1/g2 = G M1/R1^2 X 4R1^2/G2M1
g1:g2 = 4:2 = 2:1

Answer 2

Acc to law of gravitation : mg1=GM1m/R1^2

g1= GM1 / R1^2

( considering that for the first planet variables are placed with 1 and for the second with 2 )

Similarly g2 = G M2/R2^2

As we know that M2 is twice of M1 and R2 is twice of R1

So g2= G2M1/(2R1)^2

g1/g2 = G M1/R1^2 X 4R1^2/G2M1

g1:g2 = 4:2 = 2:1