Let g be the acceleration due to gravity at the earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by $2 %$ . Keeping mass of earth and angular momentum constant, then

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

g increases by 4 % and K increases by 4%

g decreases by 2 % and K decreases by 4%

g decreases by 4 % and K decreases by 2%

g increases by 2 % and K increases by 2%

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$g = \frac{G M}{R^{2}}$

$g \propto R^{- 2}$

change in $g = (- 2) (% change in R)$

=(-2)(-2)=+4%

Rotational kinetic energy,

$K = \frac{L^{2}}{2 I}$

$L = angular momentum = constant$

$I = \frac{2}{5} m R^{2}$

$K \propto R^{- 2}$

$% change in K = (- 2) (% change in R)$

$= (- 2) (- 2) = + 4 %$

Watch 3-min video & get full concept clarity