Question

If R is the radius of earth, the height at which the weight of a body becomes $1/4$ its weight on the surface of earth is :

• A. $2R$
• B. $R$
• C. $R/2$
• D. $R/4$

Answer 1

The correct option is B $R$

At surface of the Earth, weight $W_s=\frac{GMm}{R^2}$

At height, h of the Earth weight $W_h=\frac{GMm}{(R+h{)}^2}$

Now,

$W_h=\frac{W_s}{4}$

$\frac{GMm}{(R+h{)}^2}=\frac{GMm}{4R^2}$

$\frac{1}{R+h}=\frac{1}{2R}$

$R+h=2R$

$h=R$