If the earth suddenly stops revolving and all | vedclass

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

Question

(A) The rotational kinetic energy $(K_R)$ of the earth is given by $K_R = \frac{1}{2} I \omega^2$.Assuming the earth is a solid sphere,its moment of i

Vedclass · Accepted Answer

$\frac{R^2 \omega^2}{5Js}$

Vedclass · Answer

(A) The rotational kinetic energy $(K_R)$ of the earth is given by $K_R = \frac{1}{2} I \omega^2$.Assuming the earth is a solid sphere,its moment of inertia is $I = \frac{2}{5} MR^2$.Thus,$K_R = \frac{1}{2} 	imes (\frac{2}{5} MR^2) \omega^2 = \frac{1}{5} MR^2 \omega^2$.According to the problem,this energy is converted into heat to raise the temperature of the earth by $	heta$.The heat energy required is $Q = Ms	heta$.Since the energy is expressed in Joules,we use the relation $K_R = J 	imes Q$.$\frac{1}{5} MR^2 \omega^2 = J 	imes (Ms	heta)$.Canceling $M$ from both sides,we get $\frac{1}{5} R^2 \omega^2 = Js	heta$.Therefore,the rise in temperature is $	heta = \frac{R^2 \omega^2}{5Js}$.

Similar Questions

$A$ ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the track of its centre of mass?

$A$ uniform thin wooden plank $AB$ of length $L$ and mass $M$ is kept on a table with its $B$ end slightly outside the edge of the table. When an impulse $J$ is given to the end $B$,the plank moves up with the centre of mass rising a distance $h$ from the surface of the table. Then,

What is precession?

Vedclass Test Series

Exam Paper Generator

Online Exam Module