Question

Write the value of PE : KE : TE.​

Answer 1

Answer:

-2 : 1 : -1

Explanation:

PE : KE : TE = -2 : 1 : -1

Answer 2

Correct Question:

An electron is revolving around the nucleus, find the ratio of PE : KE : TE.

OR

A satellite is revolving around a planet, find the ratio of PE : KE : TE.

Solution:

Both these questions have the same answer with the same concept.

Whenever an electron or a satellite is revolving in a circular trajectory, we observe that the potential energy is twice the KE and opposite to the kinetic energy.

$\boxed{ \bf \: PE = - 2(KE)}$

Now, total energy is the sum of PE and KE :

$\sf \therefore \: TE = PE + KE$

$\sf \implies\: TE = - 2(KE) + KE$

$\sf \implies\: TE = - (KE)$

So, the ratio comes as :

$\sf \therefore \: PE : KE : TE = - 2( KE): KE : - (KE)$

$\sf \implies\: PE : KE : TE = - 2: 1 : - 1$

So, final answer is :

$\boxed{ \bf\: PE : KE : TE = - 2: 1 : - 1}$

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Now, why PE = -2KE ?

For a satellite :

$\sf \: KE = \dfrac{1}{2} m {v}^{2}$

$\implies \sf \: KE = \dfrac{1}{2} m { \bigg( \sqrt{\dfrac{GM}{r} } \bigg)}^{2}$

$\implies \sf \: KE = \dfrac{GMm}{2r}$

Now, PE will be :

$\sf \: PE = - mgh$

$\implies \sf \: PE = - m \times \dfrac{GM}{ {r}^{2} } \times r$

$\implies \sf \: PE = - \dfrac{GMm}{ r}$

$\implies \sf \: PE = - 2(KE)$

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