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From a uniform disk 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.

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Let mass per unit area of the original disc=
Thus mass of original disc=
Radius of smaller disc=.
Thus mass of the smaller disc=
After the smaller disc has been cut from the original, the remaining portion is considered to be a system of two masses. The two masses are:
M(concentrated at O), and -M(=M/4) concentrated at O'
(The negative sign indicates that this portion has been removed from the original disc.)
Let x be the distance through which the centre of mass of the remaining portion shifts from point O.
The relation between the centres of masses of two masses is given as:
(The negative sign indicates that the centre of mass gets shifted toward the left of point O) 
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Question Text
From a uniform disk 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.
Updated OnApr 16, 2023
TopicSystem of Particles and Rotational Motion
SubjectPhysics
ClassClass 11
Answer TypeText solution:1 Video solution: 3
Upvotes358
Avg. Video Duration7 min