Question

7. If there exists a planet with mass 2 times that of earth and radius 4 times that of earth then the ratio of acceleration due to gravity on this planet to that on surface of will be

a. 8:1

b. 1:16

c 4:1

d.1:8​

Answer 1

Answer:-

Let the mass of the earth be M & it's radius be R.

We know that,

g = GM/r² -- equation (1)

[ g acceleration due to gravity & G is gravitational constant ].

Given:

Mass of a planet is 2 times that of earth.

→ Mass of the planet = 2M

Also,

Radius is 4 times the earth's.

→ Radius of the planet = 4R

Let the acceleration due to gravity on this planet be g'.

Hence,

⟶ g' = G * (2M)/(4R)²

⟶ g' = G * 2M/16R²

⟶ g' = GM/R² * (2/16)

Substitute the value of GM/R² from equation (1).

⟶ g' = g * 1/8

⟶ g'/g = 1/8

⟶ g' : g = 1 : 8

Therefore, the ratio of accelerations due to gravity on the planet to the earth will be 1 : 8 (Option - d).