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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

In a certain region, the gravitational field is specified by E = (2 i + 3 j ) N/kg . Determine the work done by the gravitational field when a particle is moved on the line 3y + 2x = 5 .

Options

  1. A5 J
  2. B6 J
  3. C13 J
  4. D0

Correct answer

D. 0

Step-by-step solution

Given gravitational field E = 2 i + 3 j N/kg. The gravitational force on a particle of mass m is F = m E = m(2 i + 3 j ) . The particle is moved along the line 2x + 3y = 5 . Differentiating the equation of the line, we get 2 dx + 3 dy = 0 . The work done by the gravitational field for a small displacement d r = dx i + dy j is dW = F d r = m(2 dx + 3 dy) . Since 2 dx + 3 dy = 0 , we have dW = 0 . Therefore, the total work done by the gravitational field is 0 .

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