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The mass per unit length of a non-unifor...

The mass per unit length of a non-uniform rod of length L is given by `mu= lamdaxx2`​, where `lamda` is a constant and x is distance from one end of the rod. The distance of the center of mass of rod from this end is :-

A

`(L)/(2) `

B

`(L)/(4)`

C

`(3L)/(4)`

D

`(L)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C

`dm = mu dx = lamda x^(2)dx`
`x_(c.m) =(int xdm)/(int dm)=(underset(0)overset(L)int x lamda x^(2)dx)/( underset(0) overset(L)int lamdax^(2)dx)`
` (|(x^(4))/(4)|_(0)^(L))/(|(x^(3))/(3)|_(0)^(L))=((L^(4))/(4))/((L^(3))/(3))=(3L)/(4)`
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Knowledge Check

  • 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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    A
    2.5 m
    B
    1 m
    C
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    D
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    B
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    C
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    D
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