If the earth were to suddenly contract to fra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) According to the principle of Conservation of Angular Momentum $(COAM)$,since no external torque acts on the earth,the angular momentum remains co

Vedclass · Accepted Answer

$\frac{24}{n^2} \ hr$

Vedclass · Answer

(C) According to the principle of Conservation of Angular Momentum $(COAM)$,since no external torque acts on the earth,the angular momentum remains constant: $L = I_1 \omega_1 = I_2 \omega_2$.For a solid sphere,the moment of inertia is $I = \frac{2}{5} MR^2$. Let the initial radius be $R$ and the final radius be $R' = \frac{R}{n}$.Substituting the values:$\frac{2}{5} MR^2 \left( \frac{2\pi}{T} \right) = \frac{2}{5} M \left( \frac{R}{n} \right)^2 \left( \frac{2\pi}{T'} \right)$Simplifying the equation:$R^2 \cdot \frac{1}{T} = \frac{R^2}{n^2} \cdot \frac{1}{T'}$$\frac{1}{T} = \frac{1}{n^2 T'}$$T' = \frac{T}{n^2}$Given the initial duration of the day $T = 24 \ hr$,the new duration is $T' = \frac{24}{n^2} \ hr$.

If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,then the duration of the new day will be:

Similar Questions

Molten sodium chloride conducts electricity due to the presence of

The strongest acid among the following is:

The force $\vec{F} = 7\widehat{i} + 3\widehat{j} - 5\widehat{k}$ acts on a particle whose position vector is $\vec{r} = \widehat{i} - \widehat{j} + \widehat{k}$. What is the torque of the given force about the origin?

$A$ player kicks a football of mass $0.5 \ kg$ and the football begins to move with a velocity of $10 \ m/s$. If the contact between the leg and the football lasts for $\frac{1}{50} \ s$,then the force acted on the football should be ........... $N$.

If $P$ is the set of all real numbers $\alpha$ such that the product of the lengths of perpendiculars from $(\alpha, 1)$ to the pair of straight lines $3x^2+7xy+2y^2=0$ is $\frac{\sqrt{2}}{5}$,then the sum of the elements in $P$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module