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Fig. shown a uniform square plate from i...

Fig. shown a uniform square plate from identical squares at the corners can be removed. (a) Where is the centre of mass of the plate originally ? (b) Where is it after square 1 is removed ?
(c ) where is it after squares 1 and 2 are removed ? (d) Where is `c.m` after squares `1, 2, 3,` are removed ?
(f) Where is `c.m` after all the four squares are removed ? Answer in terms of quadrants and axes.

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The correct Answer is:
(i) at O, (ii) diagonally from O to 3 (iii) along OY', (iv) at O (v) diagonally from O to 4 (vi) at O
(i) The centre of mass remains at O as the excluded masses are symmetrically placed. (ii) CM shifts from 0 to 3 diagonally (iii) CM shifts along OY (iv) CM does not shift. (v) CM shifts diagonally from 0 to 4 (vi) CM doesnot shift
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Knowledge Check

  • From a uniform square plate the shaped portions are removed as shown in figure. The coordinates of centre of mass of the remaining plate are x,y Axes and origon are shown in figure.

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    `x lt (a)/(2), y lt (a)/(2)`
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    B
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    C
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    A
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