**Gravitational field and potential due to spherical bodies, Gauss and Poisson equations, gravitational self-energy; Two-body problem; Reduced mass;**

Questions:

**Q 1. **Two bodies of masses and are placed at a distance **d** apart. Show that at this position where the gravitational field due to them is zero, the potential is given by $V= – \frac G d(M_1+M_2+\sqrt{M_1M_2})$. **[10 marks]**

**Q 2. **The density inside a solid sphere of radius a is given by $ρ= (ρ_0 a)/r$, where $ρ_0$ is the density at the surface and $r$ denotes the distance from the centre. Find the gravitational field due to this sphere at a distance $2a$ from its centre.** [10 marks]**

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