Question

Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then

• A. g decreases by 2% and K decreases by 4%
• B. g decreases by 4% and K increases by 2%
• C. g increases by 4% and K increases by 4%
• D. g decreases by 4% and K increases by 4%

Answer 1

Answer: (C)

g increases by 4% and K increases by 4%

Answer 2

$g = \frac { G M } { R ^ { 2 } }$and $K = \frac { L ^ { 2 } } { 2 I }$

If mass of the earth and its angular momentum remains constant then $g \propto \frac { 1 } { R ^ { 2 } }$ and $K \propto \frac { 1 } { R ^ { 2 } }$ i.e. if radius of earth decreases by 2% then g and K both increases by 4%.

($g = \frac { G M } { R ^ { 2 } }$rFkk $K = \frac { L ^ { 2 } } { 2 I }$