Question

A circular disc of radius R is removed from a
bigger circular disc of radius 2R such that the
circumference of the discs coincide. The
centre of mass of the new disc is aR from the
centre of the bigger disc. The value of a is​

Answer 1

Answer:

    a = 1/3

Explanation:Dear student,

As the center of mass(COM) for the full disc at origin(0,0).

Proceed as given in attachment

Answer 2

The value of a is​ α = 1/3

Explanation

Let the circular disc placed in the x−y plane.  

Let the center of the complete disc of radius 2R be at origin and the center of the removed disc be on x=R. Let the mass of complete disc be M

Then, position vector of center of mass of smaller disc is  

x1 = Ri

Let the center of mass of the new disc be at (x,y). Then, its position vector is given by

Mass of disc is proportional to its area.

M1/M=A1/A=πR²/π4R²=1/4

Mass of new disc given by M2= M-M1 = 3/4

x = M1x1 + M2x2/ M1+M2

∴ 0 = M/4 Ri + 3M/4 (xi+yi) / M

By equating cofficients

x = -R/3 , y = 0

Distance from the centre of big disc d=R/3 = αR

∴ α = 1/3

Learn More

Area of a circular disc is 38.5 CM square find the circumference of the circular disc

https://brainly.in/question/2486162