1. A space vehicle of mass m is in a circular orbit of radius 2Re about the earth (mass me). What is the work done by an external agent to transfer it to an orbit of radius 4Re?
2. Three stars each of mass M and radius R are intially at rest and the distance between centres of any two stars is d and they form an equilateral triangle. They start moving towards the centroid due to mutual force of attraction. What are the velocities of the stars just before the collision? Radius of each star is R.
71Q1.
I'll provide you with some valuable hints.
Firstly, Let the velocity with which the satellite orbits = v. Now find the total Energy (KE+PE) of it when it is away from earth at a distance 2Re
Now when it is transferred to 4Re, it's velocity and hence (KE) doesn't remain same. Balancing the forces , you need to find it and also the PE.
Now the job is done. ΔE = W
71Q2. It is nothing but a HC verma question where three particles from the vertices of equilateral triangle moves towards each other such that their velocities are aimed to each one.
