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Question:

A body is orbiting very close to the earth surface with kinetic energy KE. The energy required to completely escape from it is

2KE

KE√2

None of the above

√2KE

Solution:

When a body is orbiting the earth, the centripetal acceleration is provided by the gravitational force of attraction from earth.
√GMmR²=mv²/R
√KE=mv²/2=GMm/2R
The gravitational potential energy=PE=-GMm/R
Hence the total energy=PE+KE=-GMm/2R
Therefore the energy that must be provided to the body to completely escape from its orbit=GMm/2R=KE