Question

The value of gravitational acceleration ‘$g$’ at a height ‘$h$’ above the earth’s surface is $\frac{g}{4}$ then ($R =$ radius of earth)

• A. $h = R$
• B. $h = \frac{R}{2}$
• C. $h = \frac{R}{3}$
• D. $h = \frac{R}{4}$

Answer 1

Answer: (A)

Value of gravitational acceleration at a height $h$ above th earth's surface is given by $g^{\prime}=g\left(\frac{R}{R+h}\right)^{2}$ $\therefore \frac{ g }{4}= g \left(\frac{ R }{ R + h }\right)^{2}$
Or $\frac{R}{R+h}=\frac{1}{2}$
Or $h + R =2 R$
$\Longrightarrow h = R$