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The density of a non-uniform rod of leng...

The density of a non-uniform rod of length `1m` is given by `rho (x) = a (1 + bx^(2))`
where a and b are constants and `0 le x le 1`.
The centre of mass of the rod will be at

A

`(3(2+b))/(4(3+b))`

B

`(4(2+b))/(3(3+b))`

C

`(3(3+b))/(4(2+b))`

D

`(4(3+b))/(3(2+b))`

Text Solution

Verified by Experts

The correct Answer is:
A
Denstiy is given as `rho(x)=a(1+bx^(2))` where a and b are cosntant and `olexle1` let `bto0`, in this cases `rho(x)=a=`constant
Hence, centre of mass will be at `x=0.5 m` (middle of the rod)
Putting, `b=0` in all the options, only (a) gives.
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