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Calculate Centre of mass of a non-unifor...

Calculate Centre of mass of a non-uniform rod with linear mass density `gamma`

`lambda(mass//"length")=kx^2`

Text Solution

Verified by Experts

For a small element dx, the linear mass density can be considered constant:

`(Mass)/("Length")=lanbda=kx^(2)" "therefore` mass of this small element dm`=lambdadx=kx^(2)dx`
`M="k"int_(0)^(L)x^(2)"dx"=(KL^(3))/(3)`
`x_(cm)=(int"x dm")/(int"dm")=("K"int_(0)^(L)x^(3)"dx")/("K"(L^(3))/(3))=(3"L")/(4)`
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