Question

A frame is formed by the uniform rods having constant linear mass density. ACB part of frame is semicircular of radius 'R' and AB is straight rod.
Centre of mass of the system from centre O of AB is at a distance​

Answer 1

Answer:

2R/(π+2).

Explanation:

Since, the radius is given as R so the diameter is 2R. Let a small portion x on the perimeter of the semicircular disc be taken at ∅ angle from the center. Hence, the total mass is concentrated in the line 2R and it behaves as the part of center of mass.

So, the mass for the side be m1=x*π*R and the distance r1=2R/π. Again, the mass m2 will be x*2R and distance r2=0(center of the line).

So, the center of mass will be [x*π*R*2R/π + x*2R*0]/x*R*(π+2) which on solving we will get the center of mass at O as 2R/(π+2).