If the linear density of rod of length 3 m varies as `lambda=2+x` then the distance of centre of gravity of the rod is………….

Options

A. `(7)/(3)m`
B. `(12)/(7)m`
C. `(10)/(7)m`
D. `(9)/(7)m`

Answer

B

Explanation

The linear density of rod varies with `(dm)/(dx)=lambda`
`therefore dm=lambdadx`
`therefore` Position of centre of mass
`x_(cm)=(intdmxxx)/(intdm)=(underset(0)overset(3)int(lamdadx)x)/(underset(0)overset(3)intlambdadx)`
`=([x^(2)+(x^(3))/(3)]_(0)^(3))/([2x+(x^(2))/(2)]_(0)^(3))=(36)/(21)=(12)/(7)m`