Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be E/2. [2023]

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Q.
Given below are two statements: [2023]

Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2} .$

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E.

In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both Statement I and Statement II are incorrect

2 Both Statement I and Statement II are correct

3 Statement I is incorrect but Statement II is correct

4 Statement I is correct but Statement II is incorrect

Ans.
(1)

$Energy of satellite in orbit E = \frac{- G M m}{2 R}$

$PE of satellite in orbit U = \frac{- G M m}{R}$

$\Rightarrow U = 2 E$

$KE of satellite in orbit K = E - U$

$K = \frac{G M m}{2 R} = (- E)$

Solution

1 Both Statement I and Statement II are incorrect

2 Both Statement I and Statement II are correct

3 Statement I is incorrect but Statement II is correct

4 Statement I is correct but Statement II is incorrect

Ans.
(1)

$Energy of satellite in orbit E = \frac{- G M m}{2 R}$

$PE of satellite in orbit U = \frac{- G M m}{R}$

$\Rightarrow U = 2 E$

$KE of satellite in orbit K = E - U$

$K = \frac{G M m}{2 R} = (- E)$

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Solution

1 Both Statement I and Statement II are incorrect

2 Both Statement I and Statement II are correct

3 Statement I is incorrect but Statement II is correct

4 Statement I is correct but Statement II is incorrect

Ans. (1) Energy of satellite in orbit E=-GMm2R PE of satellite in orbit U=-GMmR ⇒U=2E KE of satellite in orbit K=E-U K=GMm2R=(-E)

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Ans.
(1)

$Energy of satellite in orbit E = \frac{- G M m}{2 R}$

$PE of satellite in orbit U = \frac{- G M m}{R}$

$\Rightarrow U = 2 E$

$KE of satellite in orbit K = E - U$

$K = \frac{G M m}{2 R} = (- E)$