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A rod length L and mass M is placed alon...

A rod length `L` and mass `M` is placed along the `x`-axis with one end at the origin, as shown in the figure above. The rod has linear mass density `lamda=(2M)/(L^(2))x,` where `x` is the distance from the origin. Which of the following gives the `x`-coordinate of the rod's center of mass?

A

`2/3L`

B

`1/4L`

C

`1/3L`

D

`1/2L`

Text Solution

Verified by Experts

The correct Answer is:
A
`X_(cm)=1/M int x dm=1/M int_(0)^(L) x((2m)/(L^(2))x)dx=(2L)/3`
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