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\[=M-\frac{M}{4}=\frac{3M}{4}\] \[\therefore \]  \[-\frac{3M}{4}\alpha R+\frac{M}{4}R=0\] \[\Rightarrow \]               \[\alpha =\frac{1}{3}\]