Question

The mass density of a certain planet is uniform throughout the volume of the planet. If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on the mass is A : proportional to 1/r B : not dependent on r C : proportional to r2 D : proportional to 1/r2 E : proportional to r

Answer 1

Correct answer is option E ( gravitational force on the mass m will be proportional to r )

Step-by-step explanation:

Let R be the radius of planet and M be its mass

Let us consider point mass m lie at the distance x(=R-r) below planet surface,

Than, We know that

Acceleration due to gravity at distance x below the planet's surface is given as

`g=(GM)/(R^2)-(GMx)/(R^3)`........(1)

But, x=R-r

put value of x in equation 1

`g=(GM)/(R^2)-(GM(R-r)/(R^3)`

Therefore gravitational force on mass m will be given as

`gm=(GmM)/(R^2)-(GmM(R-r))/(R^3)`..............(2)

From equation 2 it is clear that gravitational force on the mass m will be directly proportional to r hence correct option is E