Question

PHYSICS
Two semicircular rings of linear mass
densities #(lambda) and 2#(lambda), and of radius 'R' each
are joined to form a complete ring. The
distance of the center of the mass of
complete ring from its centre is​

Answer 1

Answer:

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Answer 2

Answer:

Explanation:

we know that center of mass of semi circular ring  is 2r/pi

so, com of first one is 0, 2r1/pi

so,center of second one is  0,2r2/pi

we can form complete ring only if one is below other

after forming let center be 0,0

lamda1=2lamda2

m1/pir1^2=2m2/pir2^2

m1=2m2(r1/r2)^2

com of truncated bodies is

m1x1+m2x2 / m1+m2

and m1y1+m2y2 / m1+m2

Xcom=0

Ycom=m1(2r1/pi) -m2(2r2/pi) / m1+m2

m2(r1/r2)^2(2r1/pi)-m2(2r2/pi)/m1+m2

since r1=r2 and m1=2m2=m

Ycom=m1y1+m2y2/m1+m2

m(2r/pi)-m/2(2r/pi)/3m

2r/pi(m/2)/3m

r/3pi