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A circular plate of uniform thickness has a diameter of 56cm.A circular portion of diameter 42cm is removed from one edge of the plate .find the position of the center of mass of the remaining portion.

  • physics - ,

    The removed portion has 3/4 the diameter and 9/16 of the area and mass M of the full circular (56 cm dia) plate.

    Measure CM location from the center of the larger full circle. The center of the cutout circular hole is 7 cm from the center of the large circle

    [M - (9/16)M]*x = M*0 - (9/16)M*7
    (7/16)x = -63/16
    x = 63/7 = -9.0 cm

    The CM is 9 cm from the center of the large circle, in the opposite direction from the center of the removed circle

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