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2 years ago

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A planet of mass M and radius R has no atmosphere. The escape velocity at its surface is ve. An object of mass m is at rest a di

stance r from the center of the planet, where r>>R. The particle falls to the surface of the planet. The total mechanical energy of the particle at the surface of the planet is closest to

1 answer:

zubka84 [21]2 years ago

8 0

Answer:

Explanation:

Expression for escape velocity

ve = $\sqrt{\frac{2GM}{R} }$

ve² R / 2 = GM

M is mass of the planet , R is radius of the planet .

At distance r >> R , potential energy of object

= $\frac{-GMm}{r}$

Since the object is at rest at that point , kinetic energy will be zero .

Total mechanical energy = $\frac{-GMm}{r}$ + 0 = $\frac{-GMm}{r}$

Putting the value of GM = ve² R / 2

Total mechanical energy = ve² Rm / 2 r

This mechanical energy will be conserved while falling down on the earth due to law of conservation of mechanical energy . So at surface of the earth , total mechanical energy

= ve² Rm / 2 r

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