Question
Asked Oct 30, 2019
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(a) Show that the CM of a uniform thin rod of
length / and mass M is at its center. (b)
Determine the CM of the rod assuming its
linear mass density A (its mass per unit
length) varies linearly from A = at the left
end to double that value, A = 2A0, at the right
y
end.
dm λdx
X
0
х
dx
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(a) Show that the CM of a uniform thin rod of length / and mass M is at its center. (b) Determine the CM of the rod assuming its linear mass density A (its mass per unit length) varies linearly from A = at the left end to double that value, A = 2A0, at the right y end. dm λdx X 0 х dx

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Expert Answer

Step 1

(a)

Consider lambda be the uniform mass density of the rod.

From the definition of center of mass.

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xdn cm 0 Adx 시 xdr 2 10 II

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Step 2

Total length of the rod is l and the result obtained for the center of mass is l/2. Therefore, required result is proved.

Step 3

(b)

 

As the linear mass density of the rod is varying. Theref...

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24- l =+

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Physics

Centre of Mass and Centre of Gravity

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