A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the earth? (1) 48 n (2) 32 n (3) 30 n (4) 24 n

 Answer: (2) 32N

Explanation

Let’s start with the most basic scenario:

On the surface of the Earth, i.e., at a height R (where R is the radius of the Earth),

F=mg=72N.

From the universal law of gravitation we get: F=GMm/R2

⇒ mg = GMm/R2

⇒ g = GM/R2

Now, if the body is raised to a height of h=R/2 then the acceleration due to gravity at that height will be:

gh = GM(R+h)2

= GM(R+R/2)2

= 4/9(GM/R2)

⇒ gh = 4/9g

Therefore, the gravitational force acting on the body at height h is found to be:

Fh = mgh = m×4/9×g =4/9×mg = 4/9×72

⇒Fh = 32N

Hence, the correct choice would be 32 N.