The gravitational field in a region is given by E = (2i + 3j)Nkg^-1. Show that no work is done by the gravitational field whom a particle is moved on the line 3y +2x = 5.
[Hint: if a line y=mx + c makes angle θ with the X – axis, m= tan θ]

Question

The gravitational field in a region is given by V= 20N Kg^-1 (x+y).

(a) Show that the equation is dimensionally correct.

(b) Find the gravitational field at the point (x, y). Leave your answer in terms of the unit vectors i, j, k

(c) Calculate the magnitude of the gravitational force on a particle of mass 500g placed at the origin.

Philoid · Accepted Answer

The electric field is given by

The angle made by the electric field with the x axis is

The line is given by

Hence, the angle made by the line with the x-axis is

Now,

Hence, The angle between the electric filed and the line is .

Hence, there’s no component of electric field along the line and no work would be done by this field.

The gravitational field in a region is given by E = (2i + 3j)Nkg-1. Show that no work is done by the gravitational field whom a particle is moved on the line 3y +2x = 5.[Hint: if a line y=mx + c makes angle θ with the X – axis, m= tan θ]