question_answer

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 \[\alpha R\]from the centre  of the bigger disc. The value of \[\alpha \]is

A)  1/3             

B)  1/2

C)  1/6             

D)  1/4

Correct Answer: A

Solution :

 The distance of centre of mass of new disc from the centre of mass of remaining disc is \[\alpha R.\] Mass of remaining disc \[=M-\frac{M}{4}=\frac{3M}{4}\] \[\therefore \] \[-\frac{3M}{4}\alpha R+\frac{M}{4}R=0\] \[\Rightarrow \] \[\alpha =\frac{1}{3}\]