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NEET 2002 (AIPMT) · Continuous Bodies: Standard Results & Variable Density

Continuous Bodies: Standard Results & Variable Density question from NEET 2002 (AIPMT)

Q11NEET 2002 · AIPMTMedium

Continuous Bodies: Standard Results & Variable Density

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:

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Answer: (b)

  1. λ=kx\lambda = kx, so xcm=∫0Lx⋅kx dx∫0Lkx dx=L3/3L2/2=2L3x_{cm} = \frac{\int_0^L x \cdot kx\,dx}{\int_0^L kx\,dx} = \frac{L^3/3}{L^2/2} = \frac{2L}{3}
  2. xcm=2×33=2x_{cm} = \frac{2 \times 3}{3} = 2 m
  3. So the answer is (b) 2 m.
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