Question

An object is projected vertically upwards with a velocity (gr) ^1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?

(a) R/2

(b) R

(c) 2R

(d) 4R

This question was posed to me by my college director while I was bunking the class.

My question is from Gravitation in division Gravitation of Physics – Class 11

Answer 1

Right answer is (b) R

Explanation: From the law of conservation of energy, we have;

(m x v^2)/2 – (G x M x m)/R = -(G x M x m)/(R+h)

m = Mass of object

M = Mass of earth

h = Maximum height of the object

v = Velocity of projection

(m x v^2)/2 – (g x m x R) = -(g x m x R^2)/(R+h)

(g x R)/2 = (g x R x h)/(R+h)

Therefore; h = R.