By what percent the energy of the satellite has to be increased to shift it from an orbit of radius `r` to `(3r)/2`.

Options

A. `20%`
B. `40%`
C. 0.3333
D. `66.66%`

Answer

C

Explanation

B.E. of a satellite for an orbit of radius r is
`E_(1)=(GMm)/(2r)`
and for radius `(3r)/(2), E_(2)=(GMm)/(2xx(3)/(2)r)=(GMm)/(3r)`
`therefore Delta E = (GMm)/(r )[(1)/(2)-(1)/(3)]=(GMm)/(6r)`
`therefore` Percentage increase in energy `=(Delta E)/(E )=xx 100`
`=((GMm)/(6r))/((GMm)/(2r))xx100`
`= (1)/(3)xx100=33.33%`