Question

A sector cut from a uniform disk of radius 12 cm and a uniform rod of the same mass bent into shape
of an arc are arranged facing each other as shown in the figure. If center of mass of the combination
is at the origin, what is the radius of the arc?
(A) 8 cm
(B) 9 cm
(C) 12 cm
(D) 18 cm​

Answer 1

Answer:

The radius of the arc is 8 cm

Explanation:

According to the problem the radius of the disk is 12 cm and the mass of the rod is equal with the mass of the disk

Let r be the radius of the disk and m is the mass for the both, and R is the radius of the arc which we need to find

Now,

According to the formula of COM , we can say that,

m ( 2 R /π ) − m ( 4 r/3 π) /2 m =  0

=> m ( 2 R /π ) − m ( 4  x 12 /3 π) /2 m =  0

=> ( 2 R /π ) =  ( 4  x 12 /3 π)

=> R = 8