Question 278: Gravitation

Question

The radii of circular orbits of two satellites $A$ and $B$ of the earth are ' $4 R$ ' and ' $R$ ' respectively, where $R$ is the radius of earth. If the speed of satellite $B$ is 6 V , then the speed of satellite $A$ will be

Accepted Answer

We have two satellites $A$ and $B$ orbiting Earth in circular orbits.
Radius of orbit of $A$: $r_A = 4R$
Radius of orbit of $B$: $r_B = R$
Speed of $B$: $v_B = 6V$
We need the speed of $A$.
Step 1: Orbital velocity formula
For a satellite in circular orbit,
$ v = \sqrt{\frac{GM}{r}} $
where $M$ is mass of Earth and $r$ is the orbital radius.
So,
$ \frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}} $
Step 2: Plug in given values
$ \frac{v_A}{v_B} = \sqrt{\frac{R}{4R}} = \sqrt{\frac{1}{4}} = \frac{1}{2} $
Thus,
$ v_A = \frac{1}{2} v_B $
Step 3: Evaluate
$ v_A = 	frac{1}{2} 	imes 6V = 3V $
Ã¢ÂÂ Final Answer:
$ \boxed{3V} $
Option A:
3V

Answer

3 V

Answer

4 V

Answer

12 V

Answer

$\frac{3}{4} \mathrm{~V}$

Gravitation

The radii of circular orbits of two satellites A and B of the earth are ' 4 R ' and ' R ' respectively, where R is the radius of earth. If the speed of satellite B is 6 V , then the speed of satellite A will be

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