At what height above the surface of earth the value of acceleration due to gravity would be half of its value on the surface of earth? (Radius of the earth is 6400 km)

Question

At what height above the surface of earth the value of acceleration due to gravity would be half of its value on the surface of earth? (Radius of the earth is 6400 km) (A) 2561 km (B) 2650 km (C) 3200 km (D) 9800 km

Tardigrade Admin · Accepted Answer

The ratio (g'/g)=(R2/(R+h)2)=(1/2) or R+h=√2R or h=(√2-1)R or h=(0.414)×6400. ⇒ h=2650 km

Q. At what height above the surface of earth the value of acceleration due to gravity would be half of its value on the surface of earth? (Radius of the earth is 6400 km)

2561 km

2650 km

3200 km

9800 km

The ratio $\frac{g ^{'}}{g} = \frac{R ^{2}}{( R + h ) ^{2}} = \frac{1}{2}$
or $R + h = 2 R$
or $h = (2 - 1) R$
or $h = (0.414) \times 6400.$
$\Rightarrow$ h=2650 km

Q. At what height above the surface of earth the value of acceleration due to gravity would be half of its value on the surface of earth? (Radius of the earth is 6400 km)

2561 km

2650 km

3200 km

9800 km

The ratio gg′​=(R+h)2R2​=21​ or R+h=2R​ or h=(2​−1)R or h=(0.414)×6400. ⇒ h=2650 km

The ratio $\frac{g ^{'}}{g} = \frac{R ^{2}}{( R + h ) ^{2}} = \frac{1}{2}$
or $R + h = 2 R$
or $h = (2 - 1) R$
or $h = (0.414) \times 6400.$
$\Rightarrow$ h=2650 km