First slide

Motion of planets and satellites

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

Moderate

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%

Solution

$R a d i u s i s d e c r e a s e d b y 2 % i . e ., - 2 % g = \frac{G M}{R^{2}} g \propto \frac{1}{R^{2}} g \propto R^{- 2} g % = - 2 R % = - 2 (- 2 %) = + 4 % a n d K = \frac{L^{2}}{2 I} = = \frac{L^{2}}{2 (\frac{2 M R^{2}}{5})} K \propto \frac{1}{R^{2}} K \propto R^{- 2} K % = - 2 R % = - 2 (- 2 %) = + 4 %$
We are clearly given in the question that all the other quantities remain constant other than the radius of earth. So, we could conclude that earth’s mass and angular momentum remains constant.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App