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A uniform thin rod AB of length L has li...

A uniform thin rod AB of length L has linear mass density `mu (x) = a +(bx)/(L)`, where x is measured from A. If the CM of the rod lies at a distance of `((7)/(12)L)` from A, then a and b are related as :

A

`2a = b`

B

`3a = 2b`

C

`a = 2b`

D

`a = b`

Text Solution

Verified by Experts

The correct Answer is:
A
`x_(cm) = (int xdm)/(int dm)`
`rArr (7L)/(12) = (int_(0)^(L)x(a + (bx)/(L)) dx)/(int_(0)^(L) (a + (bx)/(L)) dx)`
Solving we get `2a = b`
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