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………….

If the linear density of rod of length 3 m varies as lambda=2+x then t

1.	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………….
Answer» `(7)/(3)m` `(12)/(7)m` `(10)/(7)m` `(9)/(7)m` Solution :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`