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Math Help - Non-uniform mass per unit area of a disc?

  1. #1
    Super Member fardeen_gen's Avatar
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    Non-uniform mass per unit area of a disc?

    The mass per unit area of a disc is changing as (x + 2)/π kg/m^2 where x is the distance from the centre. If radius of the disc is 4m then:

    A)mass of disc is 224/3 kg
    B)mass of disc is 122π/3 kg
    C)mass per unit area at centre is 2/π kg/m^2
    D)mass per unit area is zero at the centre

    More than one answers are correct. Please explain how to solve these types of questions too.
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  2. #2
    Junior Member
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    Quote Originally Posted by fardeen_gen View Post
    The mass per unit area of a disc is changing as (x + 2)/π kg/m^2 where x is the distance from the centre. If radius of the disc is 4m then:

    A)mass of disc is 224/3 kg
    B)mass of disc is 122π/3 kg
    C)mass per unit area at centre is 2/π kg/m^2
    D)mass per unit area is zero at the centre

    More than one answers are correct. Please explain how to solve these types of questions too.
    This is similar to a problem in another thread:

    http://www.mathhelpforum.com/math-he...s-density.html

    For this problem, the area dA of an annulus of “infinitesimal” width dx is \mathrm{d}A=2\pi x\mathrm{d}x, so the total mass is M=\int_0^4{2\pi x\left(\frac{x+2}{\pi}\right)}\,\mathrm{d}x.
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