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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

`(3L)/4`

B

`L/8`

C

`K/L`

D

`(3K)/L`

Text Solution

Verified by Experts

The correct Answer is:
A
`dm=(kx^(2))/Ldx, x_(cm)=(int_(0)^(L)xdm)/(int_(0)^(L)(kx^(2))/Ldx)=(((L^(4))/(4))/((L^(3))/(3)))=(3L)/4`
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