    Question

# A non-uniform thin rod of length L is placed along x−axis as such its one of ends at the origin. The linear mass density of rod is λ=λ0x. The distance of centre of mass of rod from the origin is:

A
L/2
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B
2L/3
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C
L/4
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D
L/5
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Solution

## The correct option is B 2L/3Given that, Density of rod λ=λ0x Length of rod = L Now, center of mass C.M=1ML∫0xdm Now, total mass M=L∫0dm M=L∫0λ0dx M=λ0L∫0xdx M=λ0[x22]L0 M=λ0L22....(I) Now, center of mass C.M=1ML∫0xdm C.M=1ML∫0x(λdx) C.M=1Mλ0L∫0x(xdx) C.M=1Mλ0[x33]L0 C.M=1Mλ0L33 Now, put the value of λ0Mfrom equation (I) C.M=1Mλ0L33 C.M=L33×2L2 C.M=2L3 Now, the distance of center of mass of rod from the origin Hence, The distance of center of mass of rod from the origin is 2L3   Suggest Corrections  0      Similar questions  Related Videos   Integrating Solids into the Picture
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