- #1
phospho
- 250
- 0
The diagram shows a pendant in the shape of a sector of a circle with center A. The radius is 4 cm and the angle at A is 0.4 radians. Three small holes of radius 0.1 cm, 0.2cm and 0.3 cm are cut away. The diameters of the holes lie along the axis of symmetry and their centers are 1, 2 and 3 cm respectively from A. The pendant can be modeled as a uniform lamina. Find the distance of the center of mass of the pendant from A. Moments about A (y = 0 due to symmetry)
x = \frac{(0.5\times4^2\times0.4)\times(\frac{2\times4\times(sin(0.2))}{0.6}) - (0.1^2\pi\times(1)) - (0.2^2\pi\times(2))-(0.3^2\pi\times(3))}{(0.5\times4^2\times0.4) - (0.1^2\pi) - (0.2^2\pi) - (0.3^2\pi)} <br /> => x = 2.66...<br />
However the answer is 2.47 :s
x = \frac{(0.5\times4^2\times0.4)\times(\frac{2\times4\times(sin(0.2))}{0.6}) - (0.1^2\pi\times(1)) - (0.2^2\pi\times(2))-(0.3^2\pi\times(3))}{(0.5\times4^2\times0.4) - (0.1^2\pi) - (0.2^2\pi) - (0.3^2\pi)} <br /> => x = 2.66...<br />
However the answer is 2.47 :s
Last edited:
