Question

A circular plate has a uniform thickness and has a diameter of 56 cm. A circular
disc of diameter 42 cm is removed from one edge of the plate. The distance of
the centre of mass of the remaining portion from the centre of the circular
plate is

Answer 1

Explanation:

New center of mass is given by:

x

com

=

m

1

−m

2

m

1

x

1

−m

2

x

2

where,

m

1

is mass of original disc

m

2

is mass of removed disc

x

1

is center of mass position of original disc

x

2

is center of mass position of removed disc

If mass per unit area=m then,

mass of original disc=m×π×(28×10

−2

)

2

mass of removed disc=m×π×(21×10

−2

)

2

x

com

==

m×π×(28×10

−2

)

2

−m×π×(21×10

−2

)

2

m×π×(28×10

−2

)

2

×0−m×π×(21×10

−2

)

2

×(7×10

−2

)

=

mπ[(28×10

−2

)

2

−(21×10

−2

)

2

)]

−mπ(28×10

−2

)

2

(7×10

−2

)

=

0.0343

−0.003087

=−0.09m

=−9cm

Center of mass shifts by 9 cm.