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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

In a certain region, the gravitational field is given by E = (5 N/kg ) i + (12 N/kg ) j . Determine the potential at the points (12 m , 0) and (0, 5 m ) assuming the potential at the origin is zero.

Options

  1. A-120 J/kg , -120 J/kg
  2. B60 J/kg , 60 J/kg
  3. C-60 J/kg , -144 J/kg
  4. D-60 J/kg , -60 J/kg

Correct answer

D. -60 J/kg , -60 J/kg

Step-by-step solution

The relation between gravitational field E and gravitational potential V is given by: dV = - E d r Integrating from the origin (0,0) to a point (x,y) : _ V(0,0) ^ V(x,y) dV = - _ (0,0) ^ (x,y) (E_x dx + E_y dy) Given E = 5 i + 12 j and V(0,0) = 0 , we get: V(x,y) - 0 = - _ (0,0) ^ (x,y) (5 dx + 12 dy) V(x,y) = -(5x + 12y) For the point (12, 0) : V(12, 0) = -(5 12 + 12 0) = -60 J/kg For the point (0, 5) : V(0, 5) = -(5 0 + 12 5) = -60 J/kg

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