Question

Hey physics Newton
Two satellites have their masses in the ratio 3:2. The radius of their circular orbits are in the ratio 1:5. What is the total mechanical energy of A and B?​

Answer 1

Given:-

• Two satellites A&B
• Ratio of masses=3:2=Ma:Mb
• Ratio of radius of circular orbit of A&B is r and 5r respectively ra:rb= r:5r

To find:-

total mechanical energy of A and B

Solution:-

We know ,

$Mechanical \: Energy (E)\ =- \frac{GMm}{2r}$

Mechanical Energy is proportional to M/r

=> Let Ea&Eb be energy of satellites A&B

$\frac{Ea}{Eb} = \frac{Ma}{Mb } \times \frac{rb}{ra}$

$\frac{3}{2} \times \frac{5}{1}$

$\frac{Ea}{Eb} = \frac{15}{2}$

Now ,we get

Ea=15

Eb=2

Therefore:-

Mechanical Energy done by A = 15

Mechanical Energy done by B =2

Answer 2

Answer:

Given:-

Two satellites A&B

Ratio of masses=3:2=Ma:Mb

Ratio of radius of circular orbit of A&B is r and 5r respectively ra:rb= r:5r

To find:-

total mechanical energy of A and B

Solution:-

We know ,

Mechanical \: Energy (E)\ =- \frac{GMm}{2r}MechanicalEnergy(E) =−2rGMm

Mechanical Energy is proportional to M/r

=> Let Ea&Eb be energy of satellites A&B

\frac{Ea}{Eb} = \frac{Ma}{Mb } \times \frac{rb}{ra}EbEa=MbMa×rarb

\frac{3}{2} \times \frac{5}{1}23×15

\frac{Ea}{Eb} = \frac{15}{2}EbEa=215

Now ,we get

Ea=15

Eb=2

Therefore:-

Mechanical Energy done by A = 15

Mechanical Energy done by B =2

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