The radii of circular orbits of two sate...

The radii of circular orbits of two satellite `A` and `B` of the earth are `4R` and `R`, respectively. If the speed of satellite `A` is `3v`, then the speed of satellite `B` will be

`(3V)/(4)`

`6V`

`12V`

`(3V)/(2)`

Text Solution

Verified by Experts

The correct Answer is:

Orbital speed of the satellite around the earth is
` v = sqrt((GM)/( r))`
where, G = universal gravitational constant, M=mass of earth , r=radius of the orbit of the satellite For satellite A
`r_A = 4R, v_A = 3V, v_A = sqrt((GM)/(r_A))` ....(i)
For satellite B
` r_B = R, v_B = ? , v_B = sqrt((GM)/(r_B))` ...(ii) Dividing equation (ii) by equation (i), we get
`v_B/v_A =sqrt(r_A/r_B) " or " v_B = v_A sqrt(r_A/r_B)`
Substituting the given values, we get
` v_B = 3V sqrt((4R)/( R)) = 6V`

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Two satellites A and B go round a planet in circular orbit of radii 4 R and R respectively. If the speed of satellite A is 4 v, then the speed fo satellite B will be

12 v

8 v

4 v

Two satellites A and B go around a planet in circular orbits of radii 4 R and R respectively. If the speed of the satellite A is 3 V, then the speed of the satellite B will be

12 V

3 V

6 V

`(3V)/(2)`

Two satellite A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3v, the speed of the satellite B will be

12 v

6 v

`(4)/(3)` v

`(3)/(2)` v