question_answer 16)

From a uniform disc of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body. 

Answer:

The situation is shown in Fig. 7.104. Let O be the CM of the original circular portion,  that of the circular e hole cut out and  that of the remaining shaded portion. Let m be the mass per unit area of the disc. Fig. 7.104   Mass of the original disc,   Mass of the circular hole cut,                 Mass of the remaining portion,   Masses  and  may be assumed to be concentrated at  and  respectively and 0 is their CM.  Moment of  about O = Moment of  about O or              or            or            Thus the CM of the resulting portion lies at R/6 from the centre of the original disc in a direction opposite to the centre of the cut out portion.