The angular velocity of rotation of a star (o | vedclass

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

Question

(C) For matter to escape from the equator of a rotating star,the centrifugal force acting on a particle of mass $m$ at the equator must be equal to th

Vedclass · Accepted Answer

$\sqrt{\frac{2GM}{R^3}}$

Vedclass · Answer

(C) For matter to escape from the equator of a rotating star,the centrifugal force acting on a particle of mass $m$ at the equator must be equal to the gravitational force acting on it.At the equator,the condition for the particle to just lift off is $m\omega^2 R = \frac{GMm}{R^2}$.However,the question asks for the angular velocity at which matter escapes,which relates to the condition where the effective gravity becomes zero.Equating the centripetal force required for circular motion at the surface to the gravitational force: $m\omega^2 R = \frac{GMm}{R^2}$.Solving for $\omega$: $\omega^2 = \frac{GM}{R^3}$.Thus,$\omega = \sqrt{\frac{GM}{R^3}}$.Note: If the question implies the velocity equivalent to escape velocity $v_e = \sqrt{\frac{2GM}{R}}$,then $\omega = \frac{v_e}{R} = \sqrt{\frac{2GM}{R^3}}$.Given the options provided,the correct expression is $\sqrt{\frac{2GM}{R^3}}$.

The angular velocity of rotation of a star (of mass $M$ and radius $R$) at which the matter starts to escape from its equator will be:

Similar Questions

For a satellite,the escape velocity is $11 \ km/s$. If the satellite is launched at an angle of $60^\circ$ with the vertical,then the escape velocity will be ........... $km/s$.

$A$ body is projected vertically upwards from the surface of the Earth with a velocity equal to one-third of the escape velocity. The maximum height attained by the body will be $...... \ km$. (Take radius of Earth $R = 6400 \ km$ and $g = 10 \ m/s^2$)

$A$ rocket is fired vertically with a speed of $4 \ km/s$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth (in $km$)? (Take radius of Earth $R = 6.4 \times 10^6 \ m$ and $g = 10 \ m/s^2$)

If ${v_e}$ and ${v_o}$ represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius $R$,then

The escape velocity for a body projected vertically upwards from the surface of the Earth is $11 \ km/s$. If the body is projected at an angle of $45^o$ with the vertical,the escape velocity will be ........... $km/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module