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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

The gravitational potential in a certain region is defined by V = 20 N/kg , (x + y) . Determine the gravitational field at a point (x, y) in terms of the unit vectors i , j , and k .

Options

  1. A-(20 i + 20 j ) N/kg
  2. B-(20 i - 20 j ) N/kg
  3. C-20 i N/kg
  4. D(20 i + 20 j ) N/kg

Correct answer

A. -(20 i + 20 j ) N/kg

Step-by-step solution

The gravitational field E is related to the gravitational potential V by the relation E = - V . E = - ( V x i + V y j + V z k ) Given V = 20(x + y) = 20x + 20y . Differentiating partially with respect to x , y , and z : V x = 20 V y = 20 V z = 0 Substituting these values, we get: E = -(20 i + 20 j ) N/kg

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