Question

The gravitational field in a region is given by equation is E = (5i +12j) N/kg. if a particle of mass 2 kg is moved from the origin to the point (12m ,5m) in this region, the change in gravitational P.E is

Answer 1

Gravitational field is given by,

$E = 5\hat{i} + 12\hat{j}$

Potential will be in two directions.

Potential in x-direction ⇒

Ex = -dv/dr

∴ dv = -Edr

∴ $V_x = -\int\ {E_x} \, dx$

∴ $V_x = -\int\ {5} \, dx$

∴ Vx = -5x

∴ Vx = -5(12)

∴ Vx = -60 V.

Potential in y-direction ⇒

Ey = -dv/dr

∴ dv =  -Eydr

∴ $V_y = -\int {E_y} \, dy$

$V_y = -\int {12} \, dy$

$V_y = -12(5) \\V_y = -60V$

Thus, Total Potential at a point = Vx + Vy = -120 V.

Now,

Change in Gravitational Potential energy = Work done = mΔV

∴ Work done = 2 × (-120)

∴ Work done = -240 J.

Hence, change in Gravitational potential energy is -240 J.

Hope it helps.

Answer 2

Answer:

Explanation:

dV=−E→.dr→  

=−(5i+12j).(12i+5j)=−(60+60)=−120

Change in gravitational potential energy dU=mdV=2(−120)=−240J