The angular velocity of rotation of star (of mass M and radius R)… - Vidyadip

MCQ

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

A
$\sqrt {\frac{{2G{M^2}}}{R}} $
B
$\sqrt {\frac{{2GM}}{g}} $
✓
$\sqrt {\frac{{2GM}}{{{R^3}}}} $
D
$\sqrt {\frac{{2GR}}{M}} $

✓

Answer

Correct option: C.

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

c
(c) Escape velocity $v = \sqrt {\frac{{2GM}}{R}} $

If star rotates with angular velocity $\omega$ then $\omega = \frac{v}{R} = \frac{1}{R}\sqrt {\frac{{2GM}}{R}} = \sqrt {\frac{{2GM}}{{{R^3}}}} $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 7. gravitation→7. gravitation — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The least count of a stop watch is $0.2\, second$. The time of $20\, oscillations$ of a pendulum is measured to be $25\, second$. The percentage error in the measurement of time will be ........ $\%$

If the length of a cylinder is $l=(4.00 \pm 0.01) cm$, radius $r =(0.250 \pm 0.001) \;cm$ and mass $m =6.25 \pm 0.01\; g$. Calculate the percentage error in determination of density.

The distance of a particle moving on a circle of radius $12 \,m$ measured from a fixed point on the circle and measured along the circle is given by $s=2 t^3$ (in meters). The ratio of its tangential to centripetal acceleration at $t=2 \,s$ is .........

The pressure inside a small air bubble of radius $0.1\, mm$ situated just below the surface of water will be equal to [Take surface tension of water $70 \times {10^{ - 3}}N{m^{ - 1}}$ and atmospheric pressure = $1.013 \times {10^5}N{m^{ - 2}}$]

A sonometer wire supports a $4\ kg$ load and vibrates in fundamental mode with a tuning fork of frequency $416Hz$. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to:

A particle has initial velocity $10\,\, m/s$. It moves due to constant retarding force along the line of velocity which produces a retardation of $5\,\, m/s^2$. Then

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $PQ$ is about ........ $kg-m^2.$

A weightless thread can bear a tension upto $3.7\,kg-wt$ . A stone of mass $500\,g$ is tied to it and revolved in a circular path of radius $4\,m$ in a vertical plane. If $g = 10\,ms^{-2}$, then the maximum angular velocity of the stone will be ......... $rad\,s^{-1}$

A particle is moving in a circle with uniform speed. Its motion is

The angular velocity of a wheel is $70\, rad/sec$. If the radius of the wheel is $0.5\, m$, then linear velocity of the wheel is ....... $m/sec$