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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` whoose mass per unit length varies as `p=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`

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 density of a non-uniform rod of length 1 m is given by rho(x)=a(1+bx^(2)) where, a and b are constants and 0lexle1 . The centre of mass of the rod will be at ………..

    A
    `(3(2+b))/(4(3+b))`
    B
    `(4(2+b))/(3(3+b))`
    C
    `(3(3+b))/(4(2+b))`
    D
    `(4(3+b))/(3(2+b))`

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