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A satallite of mass m, initally at rest ...

A satallite of mass `m`, initally at rest on the earth, is launched into a circular orbit at a height equal to the the radius of the earth. The minimum energy required is

A

`sqrt3/4` mgR

B

`1/2` mgR

C

`1/4` mgR

D

`3/4` mgR

Text Solution

Verified by Experts

The correct Answer is:
D
Energy required = Change in K.E. + change in P.E.
Also, `(GMm)/((2R)^2)=(mv^2)/(2R) rArr (GMm)/(2R) =mv^2 `
Energy required `=1/2mv^2+[(GMm)/R-(GMm)/(2R)]=(GMm)/(4R)+(GMm)/(2R)=(3GMm)/(4R)`
Also , `g=(GM)/g^2` , Hence , energy required =` 3/4 mgR`
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