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A satellite is moving with a constant sp...

A satellite is moving with a constant speed 'V' in a circular orbit about the earth. An object of mass 'm' is ejected from the satellite such that it just escapes form the gravitational pull of the earth. At the tme of its ejection, the kinetic energy of the object is

A

`(1)/(2) mV^(2)`

B

`m V^(2)`

C

`(3)/(2) mV^(2)`

D

`2m V^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Condition for object to just escape from gravitational pull of earth is that its total energy must become zero.
T.E. = K.E. + P.E.
`rArr K.E. = -P.E.`
`rArr K.E. = (GMm)/(r )` …(i)
For circular motion we can write the following equation :
`(GMm)/(r^(2)) = (mV^(2))/(r )`
`rArr r = (GM)/(V^(2))`
Substituting in equation (i) we get the following :
`K.E. = m V^(2)`
Hence option (b) is correct.
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