3. Above the earth's surface, the magnitude of the force on a particle due to the earth's gravity is inversely proportional to the square of the distance of the particle from the centre of the earth. Assuming that the earth is a sphere of radius \(R\), and taking \(g\) as the acceleration due to gravity at the surface of the earth,

1. prove that the magnitude of the gravitational force on a particle of mass \(m\) when it is a distance \(x ( x \geq R )\) from the centre of the earth is \(\frac { m g R ^ { 2 } } { x ^ { 2 } }\). A particle is fired vertically upwards from the surface of the earth with initial speed \(u\), where \(u ^ { 2 } = \frac { 3 } { 2 } g R\). Ignoring air resistance,
2. find, in terms of \(g\) and \(R\), the speed of the particle when it is at a height \(2 R\) above the surface of the earth.