Hello! Thank you for the question, The work done by the gravitational force is definitely positive as you rightly said . Since the integration is being done from infinity to r, potential in magnitude is decreasing. The difference between the gravitational potentials at r and Infinity is turning out to be negative as the potential at r is lesser when compared to infinity. Hope that helps!
At 12:30, Please explain how we are getting work done by gravitational force as negative value as force is in the same direction as displacement.
Hello! Thank you for the question, The work done by the gravitational force is definitely positive as you rightly said . Since the integration is being done from infinity to r, potential in magnitude is decreasing. The difference between the gravitational potentials at r and Infinity is turning out to be negative as the potential at r is lesser when compared to infinity.
Hope that helps!