Question

Two uniform circular discs of radii 4 cm and 2 cm respectively are attached as shown in the fig.then centre if mass of system from C1 is
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Answer 1

Answer: 6/5=0.12 cm

Explanation: $r_{com} = \frac{m_{2}r }{m_{1+m_{2} } }$

r = 4+2 = 6cm

uniform disc

Hence, surface density will be same(d)

mass(m) = surface density*area

                =d*A

$r_{com} = \frac{m_{2}r }{m_{1+m_{2} } }$

See the attachment

Answer 2

Given :

The radius of the bigger circle = 4 cm

The radius of the smaller circle = 2 cm

To find :

The center of mass of system from C1 .

Solution :

Mass density is constant .

Let mass of bigger circle be M . Then , the mass of the smaller circle will be M/4 .

Let the x coordinate of C1 be 0 .

In x axis ,

(mass of bigger circle + mass of smaller circle) * center of mass = mass of bigger circle * x coordinate of C1 + mass of smaller circle * x coordinate of C2

=> ( M + M/4 ) * center of mass = M (0) + M/4 (6)

=> center of mass = 6/5 cm

                              = 1.2 cm

The center of mass of system from C1 is 1.2 cm .