Question

An imaginary planet has a mass 5 times and radius 3 times that of the earth.what is the acceleration due to gravity on the planet,if the acceleration due to gravity on earth is 10 m/s2

Answer 1

since we know the relation g=GM/R²
the acceleration due to gravity on the imaginary planet will be equal to 5GM/(3R)²
=5GM/9R²
=5/9×10
=50/9

Answer 2

Given,

An imaginary planet has a mass 5 times and radius 3 times that of the earth.

The acceleration due to gravity on earth is 10 m/s2.

To find,

The acceleration due to gravity on the planet.

Solution,

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

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 the question and equation-1;

The acceleration due to gravity on the surface of the earth = G×M/R^2 = 10 m/s^2

Now, the acceleration due to gravity on the surface of the imaginary planet

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

= G×(5 × mass of the earth)/(3 × radius of the earth)^2

= G× 5 × (mass of the earth)/9 × (radius of the earth)^2

= 5/9 × G×(Mass of the earth)/(Radius of the earth)^2

= 5/9 × G×M/R^2 = 5/9 × 10 m/s^2

= 5.555------ m/s^2

Hence, the acceleration due to gravity on the surface of the imaginary planet is equal to 5.555------ m/s^2.