First slide

Gravitational field intensity

Question

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

Moderate

A

g increases by 2 % and K increases by 2%
B

g increases by 4 % and K increases by 4%
C

g decreases by 4 % and K decreases by 2%
D

g decreases by 2 % and K decreases by 4%

Solution

$g = \frac{G M}{R^{2}}$
$g \propto R^{- 2}$
change in $g = (- 2) (% change in R)$
=(-2)(-2)=+4%
Rotational kinetic energy,
$K = \frac{L^{2}}{2 I}$
$L = angular momentum = constant$
$I = \frac{2}{5} m R^{2}$
$K \propto R^{- 2}$
$% change in K = (- 2) (% change in R)$
$= (- 2) (- 2) = + 4 %$

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