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Centre of mass of a rod or plate with variable density

This type of question, asked 2 times: 28 Jul 2022, 28 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    28 Jul 2022

    112
    The distance of centre of mass from end AA of a one- dimensional rod (AB) having mass density ρ=ρ0(1−x2L2)kg/m\rho =\rho_{0}\left( 1 -\frac{x^{2}}{L^{2}} \right)kg/m and length LL (in meter) is 3 Lαm\frac{3\text{ }L}{\alpha}m. The value of α\alpha is (where xx is the distance from end AA )

  2. Question 2

    28 Jan 2025

    19
    The centre of mass of a thin rectangular plate (fig xx ) with sides of length aa and bb, whose mass per unit area (σ)(\sigma) varies as σ=σ0xab\sigma =\frac{\sigma_{0}x}{ab} (where σ0\sigma_{0} is a constant), would be ______\_\_\_\_\_\_

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