Could someone please expalin how to do this problem (in image): The gravitationa

Question

Could someone please expalin how to do this problem (in image):

The gravitational attraction between particles of mass m1 and m2 at a distance r apart is Gm1 m2/r2. The constant of proportionality G in the equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. The value of G is found to be G = 6.673 Times 10-11 N m2/kg2 In order to find the gravitational force between two objects, slice the objects into pieces, use this formula for the pieces, and sum using a definite integral. What is the force of gravitational attraction between a thin uniform rod of mass M and length l and a particle of mass m lying in the same line as the rod at a distance a from one end?

Explanation / Answer

alright since you asked how to solve it, here is a way.

let at distance x from the particle we consider a small peice of length dx ,

we can find the mass of these small pieces as the mass M is uniformly distributed over the length l, let the mass of this small peice dx be dM, you can then find the graviational force between this piece and the partcle, as the force between 2 particles of mass m and dM by the formula, then get the total force by integrating x form 0 to l, let me know if you face any trouble.

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