Question

A body weighs $72N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth from the surface?

• A. $72N$
• B. $28N$
• C. $16N$
• D. $32N$

Answer 1

Answer: (D)

Lrt $R_e$ be the radius of earth

Given $h=R_e/2$

Since h is comparable to $R_e$

So, $g_h=\frac{GM}{(R_e+h{)}^2}$

Putting $h=R_e/2$,we get

$\Rightarrow g_h=\frac{4}{9}\times \frac{GM}{R_e^2}=\frac{4g}{9}$

Where g is acceleration due to gravity at the surface of earth

Therefore weight at a height equal to half of the earth's radius $=\frac{4}{9}\times 72=32N$

Hence correct answer is option $D$