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The centre of mass of a non uniform rod ...

The centre of mass of a non uniform rod of length L, whose mass per unit length varies as `rho=(k.x^2)/(L)` where k is a constant and x is the distance of any point from one end is (from the same end)

A

`(3)/(4)L`

B

`(1)/(4)L`

C

`(k)/(L)`

D

`(3k)/(L)`

Text Solution

Verified by Experts

The correct Answer is:
A

`:. x_(cm)=(underset(0)overset(L)int(K)/(L)x^(2)dx.x)/(underset(0)overset(L)int (K)/(L)x^(2)dx)=((x^(4))/(4)underset(0)overset(L)|)/((x^(3))/(3)underset(0)overset(L)|)`
`=(3)/(4)L`
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