DAY 4 – DAW January

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]

Video Solution :