Question

The gravitational field in a region is given by E = (2 hati + 3 hatj) N//kg. Find the work done by the gravitiational filed when a particle of mass 1 kg is moved on the line 3y+ 2X = 5 from (1 m,1m) to (-2 m, 3m).

Answer 1

Given:

Gravitational field in a region is given by E = (2 hati + 3 hatj) N//kg

Mass = 1 kg

Moved along the line:  3y+ 2X = 5,

From ( 1,1 ) to ( -2 , 3 )

To Find:

The work done by the gravitational field

Solution:

We know, work done,

• W = F.Δr
• Force = Mass x Field = 1kg x ( 2i + 3j)
• Δr = dxi + dyj = (  -2 - 1 ) i + 3 -1 j = -3i + 2j
• W = ( 2i + 3j ) . ( -3i + 2j) = -6 + 6  = 0J.

Therefore no work is done as the force is perpendicular to the displacement.