Question

The gravitational potential in a region is given by, V = 200(X + Y) J//kg. Find the magnitude of the gravitational force on a particle of mass 0.5 kg placed at the orgin.

Answer 1

The magnitude of the gravitational force on a particle of mass 0.5 kg placed at the orgin is :

• Given : V = 200(X + Y) J/kg and mass, m = 0.5 kg

• We know that the relation between electric field and potential is given as,

E = - [ (∂V/∂X)i + (∂V/∂Y)j + (∂V/∂Z)k ]

E = - [ (∂200X/∂X)i + (∂200Y/∂Y)j ] N/kg

• Therefore,

E = (200i + 200j) N/kg

• Force, F = mE

F = 0.5×( 200i + 200j )

= ( 100i + 100j ) N

• Magnitude of gravitational force is,

|F| = √(100^2 + 100^2)

• |F| = 100√2 N