Two satellites have their masses in the ratio 3:1. The radii of their circular orbits are in the ratio 1:4. What is the total mechanical energy of A and B?
Answers
Given
✭ Mass of two Satellites are of the ratio 3:1
✭ Radii of their circular orbit are in the ratio 1:4
\displaystyle\large\underline{\sf\blue{To \ Find}}To Find
◈ Ratio of their total mechanical energy?
\displaystyle\large\underline{\sf\gray{Solution}}Solution
So here to find the total energy we may use,
\displaystyle\sf \underline{\boxed{\sf Total \ Energy = \dfrac{-GMm}{2r}}}Total Energy=2r−GMm
Also let the two Bodies be A & B
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\underline{\bigstar\:\textsf{According to the given Question :}}★According to the given Question :
We are given that,
⪼ \displaystyle\sf \dfrac{m_1}{m_2} = \dfrac{3}{1}m2m1=13
And,
⪼ \displaystyle\sf \dfrac{r_1}{r_2} = \dfrac{1}{4}r2r1=41
So then their total energy (E) will be,
➝ \displaystyle\sf E_A = \dfrac{-GMm_1}{2r_1}EA=2r1−GMm1
And
➝\displaystyle\sf E_B = \dfrac{-GMm_2}{2r_2}EB=2r2−GMm2
➳\displaystyle\sf \dfrac{\dfrac{-GMm_1}{2r_1}}{\dfrac{-GMm_2}{2r_2}}2r2−GMm22r1−GMm1
➳\displaystyle\sf \dfrac{m_1}{r_1} \times \dfrac{r_2}{m_2}r1m1×m2r2
➳ \displaystyle\sf \dfrac{m_1}{m_2} \times \dfrac{r_2}{r_1}m2m1×r1r2
➳ \displaystyle\sf \dfrac{3}{1}\times \dfrac{4}{1}13×14
➳ \displaystyle\sf \dfrac{3\times4}{1}13×4
➳\displaystyle\sf\pink{\dfrac{E_A}{E_B} = \dfrac{12}{1}}EBEA=112
\displaystyle\sf \therefore\:\underline{\sf Their \ Ratio \ will \ be \ E_A:E_B = 12:1}∴Their Ratio will be EA:EB=12:1
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hope it help you
question=>Two satellites have their masses in the ratio 3:1. The radii of their circular orbits are in the ratio 1:4. What is the total mechanical energy of A and B?
