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 :_

Options

A. `2a = b`
B. `3a = 2b`
C. `a = 2b`
D. `a = b`

Answer

A

Explanation

`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`