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The centre of mass of a non uniform rod ...

The centre of mass of a non uniform rod of length L, whose mass per unit length varies as `rho=(k.x^2)/(L)` where k is a constant and x is the distance of any point from one end is (from the same end)

A

`3L//4`

B

`L//4`

C

`2L//3`

D

`L//3`

Text Solution

Verified by Experts

The correct Answer is:
A
`bar(x) = (intxdm)/(intdm) = (int_(0)^(L) x(kx^(2))/(L)dx)/(int(kx^(2))/(L)dx) = (3L)/(4)`
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Knowledge Check

  • The centre of mass of a, non uniform rod of length L whose mass per unit length p varies as p = (kx^(2))/(L) where k: is a constant and x is the distance of any point from one end, is (from the same end):

    A
    `3/4 L`
    B
    `1/4 L`
    C
    `k/L`
    D
    `(3k)/(L)`

  • The centre of mass of a non uniform rod of length L whoose mass per unit length varies asp=kx^(2)//L , (where k is a constant and x is the distance measured form one end) is at the following distances from the same end

    A
    `3L//4`
    B
    `L//4`
    C
    `2L//3`
    D
    `L//3`

  • The mass per unit length of a non - uniform rod of length L is given mu = lambda x^(2) , where lambda is a constant and x is distance from one end of the rod. The distance of the center of mas of rod from this end is

    A
    `(L)/(2)`
    B
    `(L)/(4)`
    C
    `(3L)/(4)`
    D
    `(L)/(3)`

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