The gravitational field in a region is given by `vecg=(5hati+12hatj)"N kg"^(-1)`. The change in the gravitational potentil energy of a particle of mass 2kg when it is taken from the origin to a point `(7m, -3m)` is

Options

A. 71 J
B. `13 sqrt(58J)`
C. `- 71 ` J
D. 1 J

Answer

D

Explanation

Gravitational field , I = `(5 hati 12 hatj) `N/kg
` I = - (dv)/(dr)`
` v= - [ int_(0)^(x) I_(x) dx + int_(0)^(y) I_(y) dy ] = - [ I_(x).x + I_(y).y ] `
` = - [ 5 (7 -0) + 12 (- 3 - 0) ] `
= - `[ 35 + (- 36) ] = 1 ` J/kg
i.e., change in gravitational potential 1 J/kg.
Hence change in gravitational potential energy 1 J.