On the \(x\text-\)axis at a distance \(x\) from the origin, the gravitational field due to a mass distribution is given by \(\frac{A x}{\left(x^2+a^2\right)^{3 / 2}}\) in the \(x\)-direction. The magnitude of gravitational potential on the \(x\)-axis at a distance \(x\), taking its value to be zero at infinity, is:
1. \( \frac{A}{\left(x^2+a^2\right)^{3 / 2}} \)
2. \( A\left(x^2+a^2\right)^{1 / 2} \)
3. \( A\left(x^2+a^2\right)^{3 / 2} \)
4. \(\frac{A}{\left(x^2+a^2\right)^{1 / 2}}\)

From a solid sphere of mass \(M\) and radius \(R\), a spherical potion of radius \(\dfrac{R}{2}\) is removed, as shown in the figure. Taking gravitational potential \(V=0\) at \(r=\infty,\) the potential at the centre of the cavity thus formed is: (\(G=\) gravitational constant)
                         
1. \(\dfrac{-{GM}}{2 {R}} \)
2. \(\dfrac{-{GM}}{{R}} \)
3. \(\dfrac{-2 {GM}}{3 {R}} \)
4. \(\dfrac{-2 {GM}}{{R}}\)