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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 density of a non-uniform rod of length 1m is given by rho (x) = a (1 + bx^(2)) where a and b are constants and 0 le x le 1 . 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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