The potential energy of a system of four particles placed at the vertices of a square of side l (as shown in the figure below) and the potential at the centre of the square, respectively, are:

1.   $-5.41\frac{{\mathrm{Gm}}^{2}}{\mathrm{l}}$ and 0

2.   0 and $-5.41\frac{{\mathrm{Gm}}^{2}}{\mathrm{l}}$

3.   $-5.41\frac{{\mathrm{Gm}}^{2}}{\mathrm{l}}$ and $-4\sqrt{2}\frac{\mathrm{Gm}}{\mathrm{l}}$

4.   0 and 0

Subtopic: Â Gravitational Potential Energy |
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Two uniform solid spheres of equal radii $${R},$$ but mass $${M}$$ and $$4M$$ have a centre to centre separation $$6R,$$ as shown in the figure. The two spheres are held fixed. A projectile of mass $$m$$ is projected from the surface of the sphere of mass $$M$$ directly towards the centre of the second sphere. The expression for the minimum speed $$v$$ of the projectile so that it reaches the surface of the second sphere is:

1. $$\left(\frac{3 {GM}}{5 {R}}\right)^{1 / 2}$$
2. $$\left(\frac{2 {GM}}{5 {R}}\right)^{1 / 2}$$
3. $$\left(\frac{3 {GM}}{2 {R}}\right)^{1 / 2}$$
4. $$\left(\frac{5 {GM}}{3 {R}}\right)^{1 / 2}$$

Subtopic: Â Gravitational Potential Energy |
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