The ratio (g/g h) , where g and gh are the accelerations due to gravity at the surface of the earth and at a height h above the earth's surface respectively, is :

Question

The ratio (g/g h) , where g and gh are the accelerations due to gravity at the surface of the earth and at a height h above the earth's surface respectively, is : (A)  (1+(h/R))2  (B)  (1+(R/h))2  (C)  ((R/h))2  (D)  ((h/R))2

Tardigrade Admin · Accepted Answer

The value of acceleration due to gravity g at a height h above the surface of earth is gh=(g/(1+(h)R)2) where R is radius of earth. ∴ (g/gh)=(1+(h/R))2

Q. The ratio $\frac{g}{g h}$ , where $g$ and $g_{h}$ are the accelerations due to gravity at the surface of the earth and at a height $h$ above the earth's surface respectively, is :

$(1 + \frac{h}{R})^{2}$

$(1 + \frac{R}{h})^{2}$

$(\frac{R}{h})^{2}$

$(\frac{h}{R})^{2}$

The value of acceleration due to gravity $g$ at a height $h$ above the surface of earth is
$g_{h} = \frac{g}{( 1 + \frac{h}{R} ) ^{2}}$
where $R$ is radius of earth.
$∴ \frac{g}{g _{h}} = (1 + \frac{h}{R})^{2}$

Q. The ratio ghg​ , where g and gh​ are the accelerations due to gravity at the surface of the earth and at a height h above the earth's surface respectively, is :

(1+Rh​)2

(1+hR​)2

(hR​)2

(Rh​)2