If the angular velocity of a planet about its | vedclass

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

Question

(A) For a stationary satellite,its orbital period $T$ must be equal to the rotational period of the planet about its axis. The angular velocity of the

Vedclass · Accepted Answer

$2/3$

Vedclass · Answer

(A) For a stationary satellite,its orbital period $T$ must be equal to the rotational period of the planet about its axis. The angular velocity of the planet is $\omega = 2\pi / T$. Since the angular velocity is halved $(\omega' = \omega / 2)$,the new period $T'$ becomes $2T$ because $T = 2\pi / \omega$. According to Kepler's Third Law,the square of the orbital period is proportional to the cube of the orbital radius: $T^2 \propto r^3$. Therefore,$(T'/T)^2 = (r'/r)^3$. Substituting $T' = 2T$,we get $(2)^2 = (r'/r)^3$,which implies $4 = (r'/r)^3$. Taking the cube root on both sides,$r'/r = 4^{1/3} = (2^2)^{1/3} = 2^{2/3}$. Comparing this with $r'/r = 2^n$,we find $n = 2/3$.

If the angular velocity of a planet about its axis is halved,the distance of the stationary satellite of this planet from the centre of the planet becomes $2^{n}$ times the initial distance. Then the value of '$n$' is

Similar Questions

The Earth moves around the Sun in an elliptical orbit as shown in the figure. The ratio $OA/OB = x$. The ratio of the speed of the Earth at $B$ to that at $A$ is nearly

Weightlessness experienced while orbiting the earth in a spaceship is the result of:

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{L}$. The magnitude of the areal velocity of the planet is:

Two heavenly bodies $S_1$ and $S_2$,not far from each other,are seen to revolve in orbits:

The centripetal force acting on a satellite orbiting around the Earth and the gravitational force of the Earth acting on the satellite are both equal to $F$. The net force on the satellite is

Vedclass Test Series

Exam Paper Generator

Online Exam Module