Question

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`

Answer 1

Correct Answer - 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`