A satellite of $$10^3 \text{ kg}$$ mass is revolving in circular orbit of radius $$2R$$. If $$\frac{10^4 R}{6} \text{ J}$$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $$g = 10 \text{ m/s}^2$$, $$R$$ = radius of earth)

Satellite mass = $$10^3$$ kg, initial orbit radius = $$2R$$.

Total energy in circular orbit: $$E = -\frac{GMm}{2r}$$.

Initial energy: $$E_1 = -\frac{GM \times 10^3}{2 \times 2R} = -\frac{GM \times 10^3}{4R}$$.

Using $$GM = gR^2$$: $$E_1 = -\frac{gR \times 10^3}{4} = -\frac{10 \times R \times 10^3}{4} = -2500R$$.

Energy supplied: $$\frac{10^4R}{6}$$ J.

New energy: $$E_2 = E_1 + \frac{10^4R}{6} = -2500R + \frac{10000R}{6} = R(-2500 + \frac{5000}{3}) = R\frac{-7500+5000}{3} = \frac{-2500R}{3}$$.

$$E_2 = -\frac{GMm}{2r_2} = -\frac{gR^2 \times 10^3}{2r_2} = -\frac{10^4R^2}{2r_2}$$.

$$\frac{-2500R}{3} = \frac{-10^4R^2}{2r_2}$$

$$r_2 = \frac{10^4R^2 \times 3}{2 \times 2500R} = \frac{3 \times 10^4R}{5000} = 6R$$.

The correct answer is Option 4: $$6R$$.