Q. 194.7( 3 Votes )

The gravitational field in a region is given by

(a)Find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin.

(b)Find the potential at the points (12m,0) and (0, 5m) if the potential at the origin is taken to be zero.

(c) Find the change in gravitational Potential energy if a particle of mass 2 kg is taken from the origin to the point (12m, 5m).

(d)Find the change in potential energy If the particle is taken from (12m, 0) to (0,5m).

Answer :

Given, electric field,

(a) Mass of the particle,

The force on the particle is

The magnitude is

(b) Here, the potential at (12,0) is

And the potential at (0, 5) is

(c) The potential energy at (12,5) m is

And potential energy at the origin is zero.

therefore, the change in potential energy is

(d) From (b) we know that the potential at (12,0) is equal to the potential at (0,5). This makes an equipotential surface and hence the potential energy of the particle would be same at both the points. So, the change in potential energy is zero.

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