A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$, such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha/R$ from the centre of the bigger disc. The value of $\alpha$ is
In figure,, O is the centre of circular disc of radius $2R$ and mass $M.C_1$ is centre of disc of radius R, which is removed. If $s$ is mass per unit area of disc, then
$M=\pi\left(2R\right)^{2}\sigma$
Mass of disc removed, $M_{1}=\pi R^{2}\sigma=\frac{1}{4}M$
Mass of remaining disc, $M_{2}=M-M_{1}$$=M-\frac{1}{4}M=\frac{3}{4}M$
Let centre of mass of remining disc be at $C_{2}$ where $OC_{2} = x$
As $M_{1}\times OC_{1}=M_{2}\times OC_{2}$$\therefore \frac{M}{4}R=\frac{3M}{4}x$$x=\frac{R}{3}=\alpha R \,\therefore \alpha=\frac{1}{3}$
Was this answer helpful?
0
0
Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.
