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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

`(sqrt(3))/4 mgR`

B

`1/2 mgR`

C

`1/4 mgR`

D

`3/4 mgR`

Text Solution

Verified by Experts

The correct Answer is:
d
We know
`V_(0)=sqrt((GM)/r) & g=(GM)/(R^(2))`
From energy conservation
`U_(i)+K_(i)=U_(f)+K_(f)`
`-(GMm)/(2R)+1/2m(sqrt((GM)/(2R)))^(2)`
`K_(i)=(3GMm)/(4R)impliesK_(i)=3/4 mgR`
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