The approximate height from the surface of earth at which the weight of the body becomes (1/3) of its weight on the surface of earth is: [Radius of earth R =6400 km and √3=1.732]

Question

The approximate height from the surface of earth at which the weight of the body becomes (1/3) of its weight on the surface of earth is: [Radius of earth R =6400 km and √3=1.732] (A) 3840 km (B) 4685 km (C) 2133 km (D) 4267 km

Tardigrade Admin · Accepted Answer

Mg prime=( M /3) g g prime=( g /3) g prime= g (( R / R + h ))2=( g /3) ( R / R + h )=(1/√3) h =(√3-1) R =(1.732-1) 6400 h =4685 km

Q. The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is :
[Radius of earth $R = 6400 km$ and $3 = 1.732]$

$3840 km$

$4685 km$

$2133 km$

$4267 km$

$M g^{'} = \frac{M}{3} g$
$g^{'} = \frac{g}{3}$
$g^{'} = g (\frac{R}{R + h})^{2} = \frac{g}{3}$
$\frac{R}{R + h} = \frac{1}{3}$
$h = (3 - 1) R$
$= (1.732 - 1) 6400$
$h = 4685 km$

Q. The approximate height from the surface of earth at which the weight of the body becomes 31​ of its weight on the surface of earth is : [Radius of earth R=6400km and 3​=1.732]

3840km

4685km

2133km

4267km