Question

Which of the following is the variation of acceleration due to gravity at a height “h” above the earth’s surface? Let “R” be the radius of the earth and “M1” the mass of earth. (Assume h < < R)

(a) g = (G*M1)/R^2

(b) g = (G*M1)/h^2

(c) g = (G*M1)/(R/h)^2

(d) g = [(G*M1)/R^2] x [1 – (2h)/R)]

I got this question in quiz.

This intriguing question originated from Acceleration due to Gravity below and above the Surface of Earth in chapter Gravitation of Physics – Class 11

Answer 1

The correct choice is (d) g = [(G*M1)/R^2] x [1 – (2h)/R)]

The best I can explain: If “r” is the distance between the centre of the earth and the object at a height “h” above the earth’s surface, then;

R = R + h

And; g = (G*M1)/r^2

 = (G*M1)/(R + h)^2

 = (G*M1)/R^2 x (1 + h/R)^-2

Since h < < R;

Using binomial expansion and neglecting higher order terms, we can write the above expression as;

g = [(G*M1)/R^2] x [1 – (2h)/R)].