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Meaning of Commercial Bank.​

Answer» ALIGN="ABSMIDDLE" alt="\displaystyle\large\underline{\sf\red{Given}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clarge%5Cunderline%7B%5Csf%5Cred%7BGiven%7D%7D" title="\displaystyle\large\underline{\sf\red{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}}

◈ Ratio of their total mechanical energy?

\displaystyle\large\underline{\sf\gray{Solution}}

So here to find the total energy we may USE,

\displaystyle\sf \underline{\boxed{\sf Total \ Energy = \dfrac{-GMm}{2r}}}

Also let the two Bodies be A & B

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\underline{\bigstar\:\textsf{According to the given Question :}}

We are given that,

⪼ \displaystyle\sf \dfrac{m_1}{m_2} = \dfrac{3}{1}

And,

⪼ \displaystyle\sf \dfrac{r_1}{r_2} = \dfrac{1}{4}

So then their total energy (E) will be,

➝ \displaystyle\sf E_A = \dfrac{-GMm_1}{2r_1}

And

➝\displaystyle\sf E_B = \dfrac{-GMm_2}{2r_2}

➳\displaystyle\sf \dfrac{\dfrac{-GMm_1}{2r_1}}{\dfrac{-GMm_2}{2r_2}}

➳\displaystyle\sf \dfrac{m_1}{r_1} \times \dfrac{r_2}{m_2}

➳ \displaystyle\sf \dfrac{m_1}{m_2} \times \dfrac{r_2}{r_1}

➳ \displaystyle\sf \dfrac{3}{1}\times \dfrac{4}{1}

➳ \displaystyle\sf \dfrac{3\times4}{1}

➳\displaystyle\sf\pink{\dfrac{E_A}{E_B} = \dfrac{12}{1}}

\displaystyle\sf \therefore\:\underline{\sf Their \ Ratio \ will \ be \ E_A:E_B = 12:1}

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