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A uniform quarter disc of radius a lies in the first quadrant with its corner at the origin (bounded by the two coordinate axes). Its centre of mass is located at (x*a/(3*pi), x*a/(3*pi)). Find the integer value of x.

1. 2
2. 3
3. 4
4. 6

Correct answer: 4

Solution

The centre of mass of a uniform quarter disc of radius a is at (4a/(3*pi), 4a/(3*pi)), so comparing with x*a/(3*pi) gives x = 4.

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