First slide

Law of conservation of angular momentum

Question

If the Earth shrinks such that its density becomes 8 times to the present value, then the new duration of the day in hours will be

Moderate

A

24
B

12
C

6
D

4

Solution

$d_{2} = 8 d_{1} \Rightarrow \Rightarrow \frac{d_{2}}{d_{1}} = 8; M = \frac{4}{3} π R^{3} d \Rightarrow \Rightarrow d \infty \frac{1}{R^{3}}$

${(\frac{R_{1}}{R_{2}})}^{3} = \frac{d_{2}}{d_{1}} = 8; I_{1} ω_{1} = I_{2} ω_{2}$

$\frac{2}{5} M R_{1}^{2} \frac{2 π}{T_{1}} = \frac{2}{5} M R_{2}^{2} \frac{2 π}{T_{2}}$
$\frac{T_{2}}{T_{1}} = {(\frac{R_{2}}{R_{1}})}^{2} \frac{T_{2}}{24} = {(\frac{1}{2})}^{2} T_{2} = 6 hrs$

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