The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is \(9 : 4\). The mass of the planet is \(\dfrac{1}{9}\text{th}\) of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?
(Take the planets to have the same mass density)
1
\(\dfrac{R}{3}\)
2
\(\dfrac{R}{2}\)
3
\(\dfrac{R}{4}\)
4
\(\dfrac{R}{9}\)