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NEET2002PhysicsCenter of Mass, Momentum and CollisionActual

A rod of length is 3 ~m and its mass acting per unit length is directly proportional to distance x from one of its end, then its centre of gravity from that end will be at:

Options

  1. A1.5 ~m
  2. B2 ~m
  3. C2.5 ~m
  4. D3.0 ~m

Correct answer

B. 2 ~m

Step-by-step solution

Here r=k x where k= constant mass of small element of d x length is aligned & d m=k x d x & X _ CM = x d m d m = ₀^3 x(x d x) ₀^3 x d x &= [ x^3 3 ]₀^3 [ x^2 2 ]₀^3 = 27 3 9 2 =2 aligned

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