Q1- Neutron stars are extremely dense objects with a mass comparable to the mass of the sun but a radius of only several thousand meters. Consider a neutron star of mass M = 1.99*10³⁰ kg and a radius of R = 10.2 km.

(a) What is the gravitational acceleration near the surface of the star?

(b) If an incredibly heat resistant object was dropped near the surface of the star, how fast would it be going after it had fallen a distance of h = 1.5 m?

(c) Assuming uniform density, how much would 1.2 cubic centimeters of neutron star material weigh on the surface of the earth?

Q2- Two masses m₁ and m₂ (m₁+m₂ = m) are separated by a distance r₀. On releasing under the force of gravity they start moving from rest. Find their velocities when the separation between them is r (r < r₀)

Solution: