Question

At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R = radius of earth) [MP PMT 2001]
A) 2 R B) R C) 1.414 R D) 0.414 R

Answer 1

Answer is C please mark as brainleist

Answer 2

SOLUTION

Option c

• 1.414

Acceleration due to gravity at height

$\frac{g}{g} = (\frac{r}{r \: + h \: }) \\ o r \: given \: g \: = \: \frac{g}{2} or \frac{g}{g} = \frac{1}{2}$

BECAUSE,,

$( \frac{r}{ \: r \: + \: h \: } ) \: {}^{2} \\ = \frac{1}{2} or \: \frac{1}{2}or \: r + h = \sqrt{2r}$

h = √ 2 - 1 R = 0.414 R

So,,

height above ground= 0.414 R

Distance from center R + 0.414 R = 1.414 R