Question

The value of acceleration due to gravity (g) at a height h above the surface of earth is given by $g ^ { \prime } = \frac { g R ^ { 2 } } { ( R + h ) ^ { 2 } }$ If $h < < R$ then

• A. $g ^ { \prime } = g \left( 1 - \frac { h } { R } \right)$
• B. $g ^ { \prime } = g \left( 1 - \frac { 2 h } { R } \right)$
• C. $g ^ { \prime } = g \left( 1 + \frac { h } { R } \right)$
• D. $g ^ { \prime } = g \left( 1 + \frac { 2 h } { R } \right)$

Answer 1

Answer: (B)

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

Answer 2

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

$g ^ { \prime } = g \left( 1 - \frac { 2 h } { R } \right)$ ( if $\frac { h } { R }$.)