Question

At what height ${}^{\prime }{h}^{\prime }$ from the earth surface, acceleration due to gravity becomes half as that of acceleration due to gravity on the surface of earth.
[$R$ = Radius of earth]

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

Answer 1

The correct option is D $h=\frac{R}{4}$

Given,

$g^{\prime }=\frac{g}{2}$

$R=$radius of the earth

$h=$height

The acceleration due to gravity at the height $h$ is given by

$g^{\prime }=g(1-\frac{2h}{R})=\frac{g}{2}$

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

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

$h=\frac{R}{4}$

The correct option is D.