A circular metal plate of uniform thickness has a radius of 10 cm. A hole of radius 4 cm is punched on the plate a little away from its centre. Centres of the plate and of the hole are 5 cm apart. Find the centre of gravity of the plate with the hole.

A circular metal plate of uniform thickness has a radius of 10 cm. A h

1.	A circular metal plate of uniform thickness has a radius of 10 cm. A hole of radius 4 cm is punched on the plate a little away from its centre. Centres of the plate and of the hole are 5 cm apart. Find the centre of gravity of the plate with the hole.
Answer» Solution :Centre of gravity of the plate before the hole was punched was at its centre G Fig. The centre of gravity of the CIRCULAR part before the PUNCHING was at its centre `G_(1)`. Suppose the centre of gravity of the plate with the hole is at `G_(2)` on the line `GG_(1)`. Let `W_(1)` = weight of the plate with hole, `W_(2)` = weight of the disc that is cut off. `:. " " W_(1)xxGG_(2)=W_(2)xxGG_(1)" ""or",GG_(2)=(W_(2))/(W_(1))xxGG_(1)` But `GG_(1)=5 CM, W_(1)= pi(10^(2)-4^(2))xxrho(rho` = weight per unit AREA) and `W_(2)=pixx4^(2)xxrho` `:." "GG_(2)=(4^(2))/(10^(2)-4^(2))XX5=(20)/(21)`cm Hence the centre of gravity of the system will be `(20)/(11)` cm to the left of the centre of the plate.