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Q. A semi-circular disc has a variable mass distribution varying as s=(s0)sinx where (s0) is the areal mass density(initial) and x is the angle with the radius. If the radius of the dic is R. FInd its Center of mass.

Q.
A semi-circular disc has
a variable mass distribution
varying as s=(s0)sinx
where (s0) is the areal mass density(initial) and x is the
angle with the radius.
If the radius of the dic is R.
FInd its Center of mass.

Grade:12

1 Answers

Pramod J AskiitiansExpert-IIT-B
36 Points
10 years ago

Dear student,

due to symmetry x coordinate is 0

r of C.M = int{r*dm}/M

            = int{r*s0sinx*r^2dx}/M (x varies from 0 to 9)

r is same as y since x coordinate is 0

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