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

Options

A. `-450 J`
B. `-480 J`
C. `-240 J`
D. `-500 J`

Answer

B

Explanation

Given, `E = (5 hat(i) + 12 hat(j)) N kg^(-1), m = 2kg` and `r = (12 hat(i) + 15hat(j))m`
Gravitational potential,
`V = - int_(0)^(r )E. dr`
`= -int_(0)^(r ) (E_(x)hat(i) + E_(y)hat(j)) (d r_(x) hat(i) + d r_(y) hat(j))`
`V = -[ int_(0)^(x) E_(x) dr_(x) - + int_(0)^(y) E_(y)dr_(y)]`
`V = -[5 int_(0)^(12) dr_(x) + 12 int_(0)^(15) dr_(y)`
`V = -[5(12 - 0) + 12(15 - 0)]`
`V = -240 J kg^(-1)`
Hence, the change in gravitational potential energy of particle of 2 kg mass,
`E = m V = - 2 xx 240 = -480 J`
So, the correct option is (b).