Question

mass of a planet is twice that of the earth and its radius is four times of the earth .Find the value of 'g 'on its surface

Answer 1

g = GM / r^2

g1 / g2 = (M1 / M2) * (r2 / r1)^2

g2 = g1 * (r1 / r2)^2 * (M2 / M1)
= 9.8 * (r1 / (4r1))^2 * (2M1 / M1)
= 9.8 * (1/16) * 2
= 1.225 m/s^2

Value of g of that planet is 1.225 m/s^2

Answer 2

Given,

Mass of a planet = 2 × mass of the earth

The radius of the planet = 4 × radius of the earth

To find,

The value of acceleration due to gravity on the surface of the planet.

Solution,

We can simply solve this numerical problem by using the following process:

Let us assume that the acceleration due to gravity on the surface of the earth is g and on the surface of the planet is a.

As per gravitational law;

The gravitational force acting between two bodies of mass M and m, separated by a distance d, is mathematically represented as;

F = (G ×M×m)/R^2,

where G = Gravitational constant

= 6.67408 × 10-11 m3 kg-1 s-2

M = mass of the earth or planet of

concern

m = mass of the body

R = radius of the earth or planet of

concern

=> mass of the body (m) × acceleration due to gravity on the surface of the earth or planet = (G ×M×m)/R^2

=>acceleration due to gravity on the surface of the earth or planet = G×M/R^2

{Equation-1}

Now, according to equation-1;

acceleration due to gravity on the surface of the earth = G×M/R^2 = 9.8 m/s^2

{Equation-2}

And,

acceleration due to gravity on the surface of the planet

= G×(Mass of the planet)/(Radius of the planet)^2

= G×(2 × mass of the earth)/(4 × radius of the earth)^2

= G× 2 × (mass of the earth)/16 × (radius of the earth)^2

= 1/8 × G×(Mass of the earth)/(Radius of the earth)^2

= 1/8 × G×M/R^2 = 1/8 × 9.8 m/s^2

= 1.225 m/s^2

Hence, the acceleration due to gravity on the surface of the planet is equal to 1.225 m/s^2.