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Question

# The centre of mass of a non uniform rod of length L whose mass per unit length varies as ρ= kx2/L (where k is a constant and x is the distance measured from one end) is at the following distance from the same end

A
3L/4
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B
L/4
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C
2L/3
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D
L/3
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Solution

## The correct option is A 3L/4Given, density of rod is ρ=kx2LConsider small distance ds centre of mass is dm dm=ρdxdm=kx2LdxNow centre of mass od non uniform rod is , dm=ρdx∫dm=∫L0xdm∫L0dmSubstitute value of dm in above equation therefore, M=∫L0xkx2Ldx∫L0kx2LdxM=∫L0x3dx∫L0x2dxM=[x44]L0[x33]L0M=3L4Distance from the centre of mass is 3L/4Hence, correct option is (A)

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