Question

Distance between the centres of two stars is 10



a. The masses of these stars are m and 16 m and their radii a and 2a respectively. A body of mass m is fired straight from the surface of the larger star towards the smaller star.What should be its minimum initial speed to reach the surface of the smaller star ? Obtain the expression in terms of g, m and



a.

Answer 1

20 answer ha OK bye

Answer 2

Let there are two stars 1 and 2 as shown  below :

(IMAGE 1)

Let P is a point between C1 and C2 where gravitational field strength is zero. Or at P field strength due to star 1 is equal and opposite to the field strength due to star 2. Hence, (IMAGE 2)

Now, the body of mass m is projected from the surface of larger star towards the smaller one. Between C2 and P it is attracted towards 2 and between C1 and P it will be attracted towards 1. Therefore, the body should be projected to just cross point P because beyond that the particle is attracted towards the smaller star itself.

From conservation of mechanical energy mv2/2 = Potential energy of the body at P - Potential energy at the surface of the larger star.(IMAGE3)