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JEE MainPhysicsGravitation

Two separate systems of particles are considered. System 1 consists of 3 identical particles, each of mass m , placed at the vertices of an equilateral triangle of side a . System 2 consists of 4 identical particles, each of mass m , placed at the vertices of a regular tetrahedron of side a . An external agent does work W₁ to expand System 1 such that its side length becomes 2a . Similarly, work W₂ is done to expand

Options

  1. A3 4
  2. B2
  3. C1 2
  4. D1

Correct answer

C. 1 2

Step-by-step solution

The work done by an external agent equals the change in the gravitational potential energy of the system: W = U_f - U_i . For System 1 (equilateral triangle): There are ^3C₂ = 3 pairs of interacting masses. Initial potential energy, U_ 1i = - 3Gm^2 a Final potential energy, U_ 1f = - 3Gm^2 2a Work done, W₁ = U_ 1f - U_ 1i = 3Gm^2 2a For System 2 (regular tetrahedron): There are ^4C₂ = 6 pairs of interacting masses (since a tetrahedron has 6 edges). Initial potential energy, U_ 2i = - 6Gm^2 a Final potential energy,

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