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Question

Consider a non-uniform rod of length L, whose mass per unit length λ varies as λ=k.x2L where k is a constant and x is the distance of any point on rod from its one end. Then the centre of mass of rod is at (from the same end as x)

A
34L
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B
38L
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C
kL
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D
3kL
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Solution

The correct option is A 34L
consider an elemental particle of mass dm and length dx at distance x from one end,

dm=λ d x
dm=k x2 dxL

By definition
Xcm= x dm dm
=0Lkx3Ldx0L kx2L dx
=L44L33
Xcm=3L4

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