Which of the following most closely depicts the correct variation of the gravitation potential \({V(r)}\) due to a large planet of radius \({R}\) and uniform mass density? (figures are not drawn to scale)
1. 3.
2. 4.

 
Subtopic:  Gravitational Potential |
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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. \(\frac{A}{\left(x^2+a^2\right)^{1 / 2}}\)

Subtopic:  Gravitational Potential |
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