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)

• A. 2 R
• B. R
• C. 1.414 R
• D. 0.414 R

Answer 1

Answer: (D)

0.414 R

Answer 2

$g ^ { \prime } = g \left( \frac { R } { R + h } \right) ^ { 2 } \Rightarrow \frac { 1 } { \sqrt { 2 } } = \frac { R } { R + h }$

⇒ $R + h = \sqrt { 2 } R$ $\Rightarrow h = ( \sqrt { 2 } - 1 ) R = 0.414 R$