DAY 4 – DAW January

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


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=−Gd(M1+M2+M1M2)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=(ρ0a)/rρ= (ρ_0 a)/r, where ρ0ρ_0  is the density at the surface and rr denotes the distance from the centre. Find the gravitational field due to this sphere at a distance 2a2a from its centre. [10 marks]

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