The gravitational field in a region is given by ( E =(5 i +12 j ) Nkg ⁻¹ ). If a particle of mass (2 ~kg ) is moved from the origin to the point ((12 ~m ), (15 ~m ) ) in this region, the change in gravitational potential energy is

Step-by-step solution

Given, ( E =(5 i +12 j ) Nkg ⁻¹, m=2 ~kg ) and ( r =(12 i +15 j ) m ) Gravitational potential, ( aligned V & =- ₀^r E d r & =- ₀^r (E_x i +E_y j ) (d r_x i +d r_y j ) V & =- [ ₀^x E_x d r_x+ ₀^y E_y d r_y ] V & =- [5 ₀¹² d r_x+12 ₀¹⁵ d r_y ] V & =-[5(12-0)+12(15-0)] V & =-240 ~J ~kg ⁻¹ aligned ) Hence, the change in gravitational potential energy of particle of (2 ~kg ) mass, (E=m V=-2 240=-480 ~J ) So, the correct option is (b).