Mass is non-uniformly distributed over the rod of length l . Its linear mass density varies linearly with length as λ = k x 2 . The position of centre of mass (from lighter end) is given by-

Question

Mass is non-uniformly distributed over the rod of length l . Its linear mass density varies linearly with length as λ = k x 2 . The position of centre of mass (from lighter end) is given by-, 2 l / 5, 3 / l, 3 l / 4, 2 l / 3

MARKS App · Accepted Answer

X c m = ∫ x d m ∫ d m X c m = ∫ x λ d x ∫ λ d x X c m = ∫ 0 1 x k x 2 d x ∫ 0 1 k x 2 d x X c m = l 4 / 4 l 3 / 3 = 3 4 l

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