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Center of Mass as an Average Point

ntthe linear ...

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ntthe linear mass density d of a rod of length l kepth along x axis varies as d=a+bx , where a and b are positive constants. the centre of mass of the rod is atn

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Q. A rod of length

L

is placed along the

x-axis

x = 0

x = L

. The linear mass density

(mass/length)

ρ

of the rod varies with the distance

x

from the origin as

ρ = a + b x

a

b

are constants. Find the position of centre of mass of this rod.

Q. If the linear mass density of a rod of length

L

lying along x-axis and origin at one end varies as

λ = A + B x

A

B

are constants, find the coordinates of the centre of mass.

Q. A rod of length

6 m

is placed along the

x -

x = 0

x = 6 m

. The linear density (mass/length)

λ

of the rod varies with the distance

x

from the origin as

λ = k (10 - x)

k

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

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. 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.

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