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Density

If the linear...

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If the linear density of a rod of length L varies as λ = kx where k is a constant and x is the distance of any point from one end placed at origin. The distance of centre of mass from x = 0 is

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Q. A rod of length

L

is placed along the

x -

x = 0

x = L

. The linear density (mass/length)

λ

of the rod varies with the distance

x

from the origin as

λ = k x^{2}

k

is a positive constant. Find the position of the centre of mass of this rod.

Q. The centre of mass of a non uniform rod of length L whose mass per unit length

λ

λ = {k x}^{2}

where k is a constant & x is the distance of any point on rod from left end A is (from the same end)

Q. The density of a linear rod of length

L

ρ = A + B x

x

is the distance from the left end. Its centre of mass is at a distance (from the left end) of

Q. A non-uniform thin rod of length

10 m

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x

- axis such that one of its ends is at the origin. The linear mass density of the rod varies with respect to distance from the end as

λ = l_{0} x

l_{0}

is a constant. Then the position of the centre of mass of the rod w.r.t the origin will be:

Q. Calculate the centre of mass of a non-uniform rod whose linear mass density

(λ)

λ = \frac{λ_{o}}{L} x^{2}

λ_{0}

L

is the length of the rod and

x

distance is measured from one end of the rod..

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