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A metal rod extends on the x-axis from x...

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`:-`

A

`16kg`

B

`22kg`

C

`28kg`

D

`32kg`

Text Solution

Verified by Experts

The correct Answer is:
B
`(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`
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