Question

If mass of earth is decrease by 25 % and its radius is increased by 50 %then the acceleratin due to gravity at its surface by nearly

Answer 1

Acceleration due to gravity B given by,

g = GM/R

The question says that the mass is decreased by 25% and at the same time the radius is increased by 50%

Then the new mass will be

M' = (M - 25M/100)

= M' = 75M/100 = 3/4 M

The new radius will be R' = (R + 50R/100)

= R' 150R/100 = 3/2R

After this the new acceleration  because of the gravity

g' = G 3/4 M/ 3/2 R

= GM/R 3/1 x 2/3 1/2

= g' = 1/2 g

= g' 50% of g