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In a certan region of space the gravitaional field is given by -k/r where r is the distance and k is a constant. if the gravitational potential at r= a be v then what is the expression for gravitational potential ?

Answer 1

#U(r) = k ln(r/a) + V#

If the gravitational field is inverse (as opposed to inverse-square), then:

The increase in potential #Delta U# of a unit mass that is forced to move from #rho = a# to #rho = r#, where #r > a#, will equal the work done on that unit mass:

#delta W = bb F * bb x#

#Delta U = W = int_C bb F * d bb x#

#Delta U(r) = int_(rho = a)^r \ k/rho \ d rho = (k ln rho)_a^r = k ln(r/a)#

Because #U(a) = V#:

#U(r) = Delta U(r) + V#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.