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JIPMER2015PhysicsCenter of Mass, Momentum and Collision

The density of a rod having length l varies as =c+d x , where x is the distance from the left end. The centre of mass is

Options

  1. A3 c l+2 D l^2 3(2 c+D l)
  2. B2 c l+3 D l^2 2(4 c+8 l)
  3. C2 c l+3 D l^2 3(2 c+l)
  4. Dc l+D l^2 3(2 c+D l)

Correct answer

A. 3 c l+2 D l^2 3(2 c+D l)

Step-by-step solution

Let the cross-sectional area is . The mass of an element of length d x located at a distance x away from the left end is (C+D x) d x . The x -coordinate of the centre of mass is given by X_ c m = x d m d m aligned = & ₀^1 x(C+D x) d x ₀^1(C+D x) d x = & C l^2 2 + D l^3 3 C l+ D l^2 2 = 3 C l+2 D l^2 3(2 C+D l) aligned

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