A person brings a mass if 1kg from infinity to a point A. Initially, the mass was at rest but it moves at a speed 3m/s as it reaches A. The work done by the person on the mass is -5.5 J. The gravitational potential at A is

a) -1 J/kg

b) -4.5 J/kg

c) -5.5 J/kg

d) -10 J/kg

Gravitiaonal Potential is the amount of energy needed to bring  a unit mass from infinity to that point without causing any change in its velocity.

Thus, The work Done by the man on the particle  = (Gravitational Potential at that point + Kinetic Energy of the particle)

-5.5 J -Kinetic Energy of the sytem = Gravitational Potential at that point.

-5.5 - 4.5 J(Kinetic Energy of the particle) = Gravitational Potential at that point.

-10 J/kg (Option (d) might be  the answer)

Did not understand!!!

Gravitational potential + kinetic energy of particle =workdone

given to us workdone=-5.5 J

and kinetic energy=(m) * square(v) /2

so,here v=3

square(v)=9

mass=1

so kinetic energy=4.5

so, Gravitational potential=-5.5-4.5=-10 J/kg