If the gravitational field in the space is given as - K r 2 . Taking the reference point to be at r = 2 cm with gravitational potential V = 10 J kg - 1 . Find the gravitational potentials at r = 3 cm

Question

If the gravitational field in the space is given as - K r 2 . Taking the reference point to be at r = 2 cm with gravitational potential V = 10 J kg - 1 . Find the gravitational potentials at r = 3 cm in SI unit (Given, that K = 6 J cm kg - 1 )

TestHub · Accepted Answer

Given, E = - K r 2 Gravitational field and gravitational potential is related as E = - d V d r So, - d V d r = - K r 2 Integrating the above relation, ∫ 10 V d V = ∫ 2 3 K r 2 d r ⇒ V - 10 = K 1 2 - 1 3 ⇒ V - 10 = K 6 ⇒ V = 6 6 + 10 ⇒ V = 11 J kg - 1

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