First slide

Acceleration due to gravity and its variation

Question

If the radius of earth decrease by 10% , the mass remaining unchanged , then the acceleration due to gravity

Easy

A

decrease by 19%
B

increase by 19%
C

decrease by more than 19%
D

increase by more than 19%

Solution

$R_{2} = R_{1} - 10 % R_{1} = R_{1} - \frac{10}{100} R_{1} = R_{1} - 0.1 R_{1} = 0.9 R_{1} g = \frac{G M}{R^{2}} \Rightarrow g α \frac{1}{R^{2}} \Rightarrow \frac{g_{2}}{g_{1}} = {(\frac{R_{1}}{R_{2}})}^{2} \Rightarrow (\frac{g_{2}}{g_{1}} - 1) 100 = [{(\frac{R_{1}}{R_{2}})}^{2} - 1] \times 100 \Rightarrow g % = [{(\frac{R_{1}}{0.9 R_{1}})}^{2} - 1] \times 100 = [\frac{1}{0.81} - 1] \times 100 = = [\frac{1 - 0.81}{0.81}] \times 100 = [\frac{0.19}{0.81}] \times 100 = 23.45 %$

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