A metal rod extends on the `x-`axis from `x=0m` to `x=4m`. Its linear density `rho` (mass`//`length) id not uniform and varies with the distance `x` from the origin according to equation `rho=(1.5+2x)kg//m` What is the mass of rod`:-`

Options

A. `16kg`
B. `22kg`
C. `28kg`
D. `32kg`

Answer

B

Explanation

`(dm)/(dx)=(1.5+2x)rArrm=int_(0)^(4)(1.5+2x)dx`
`implies m={:(4),(0):}[1.5x+(cancel(2)x^(2))/(cancel(2))]`=1.5(4)+16=22kg`