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Question 30543
JEE Physics · Hard

Center of Mass, Momentum and Collision: COM — Continuous Body MCQ

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COM — Continuous BodyHardQuestion 30543

Question

A thin rod of non-uniform density: λ(x) = 2x (kg/m), from x = 0 to x = L. Position of COM from x = 0:
  1. A
    L/2
  2. B
    2L/3
    Correct
  3. C
    L/3
  4. D
    3L/4

Correct answer

2L/3

Explanation

x_cm = ∫₀ᴸ x λ(x) dx / ∫₀ᴸ λ(x) dx = ∫₀ᴸ 2x² dx / ∫₀ᴸ 2x dx = (2L³/3)/(L²) = 2L/3.

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