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Question

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut - off, the coordinates of the centre of mass of the remaining portion will be

  1. (2a3,2b3)
  2. (5a12.5b12)
  3. (3a4.3b4)
  4. (5a3.5b3)


Solution

The correct option is B (5a12.5b12)
The given rectangular thin sheet ABCD can be drawn as shown in the figure below,

Here,
Area of complete lamina , A1=ab
Area of shaded part of lamina =a2×b2=ab4
(x1,y1) = coordinates of centre of mass of complete lamina =(a2,a2)
(x2,y2)= coordinates of centre of mass of shaded part of lamina =(3a4,3a4)
Using formula for centre of mass, we have
XCM=A1x1A2x2A2A2
=ab(a2)ab4(3a4)abab4=8a2b3a2b163ab4=5a12
Similalry, YCM=A1y1A2y2A1A2
=ab(b2)ab4(3b4)abab4=5b12

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