Question

At what altitude in metre will the acceleration due to gravity be 25% of that at the earth's surface (Radius of earth = R metre)

• A. $\frac { 1 } { 4 } R$
• B. R
• C. $\frac { 3 } { 8 } R$
• D. $\frac { R } { 2 }$

Answer 1

Answer: (B)

R

Answer 2

$g ^ { \prime } = g \left( \frac { R } { R + h } \right) ^ { 2 }$ ⇒ $\frac { g } { 4 } = g \left( \frac { R } { R + h } \right) ^ { 2 }$⇒ $\frac { 1 } { 2 } = \frac { R } { R + h }$

⇒ $R + h = 2 R$ ∴ $h = R$