Question

The decrease in the value of g on going to a height $\frac{R}{2}$ above the earth's surface will be:

• A. $g/2$
• B. $5g/9$
• C. $4g/9$
• D. $g/3$

Answer 1

The correct option is B $5g/9$

$g=\frac{GM}{R^2}$

$g$ at height $h$

$g_h=\frac{GM}{{(R+h)}^2}(n=R/2)$

$g_h=\frac{GM}{{(R+\frac{R}{2})}^2}=\frac{4GM}{9R^2}=\frac{4g}{9}$

decrease in value of $g=g-\frac{4g}{9}=\frac{5g}{9}$.