question_answer

Two identical discs of mass m and radius r are arranged as shown in the figure. If \[\alpha \] is the angular acceleration of the lower disc and \[{{a}_{cm}}\] is acceleration of centre of mass of the lower disc, then relation between  

A) \[{{a}_{cm}}=\alpha /r\]

B) \[{{a}_{cm}}=2\alpha r\]

C) \[{{a}_{cm}}=\alpha r\]

D) None of these

Correct Answer: B

Solution :

[b]   \[Tr=\frac{m{{r}^{2}}}{2}{{\alpha }_{1}}\]        ??(1) \[Tr=\frac{m{{r}^{2}}}{2}\alpha \]                ??. (2) \[{{\alpha }_{1}}=\alpha \]                             ??. (3)                     Acceleration of point b= acceleration of point a \[r{{\alpha }_{1}}={{a}_{cm}}-r\alpha \] Hence, \[2r\alpha ={{a}_{cm}}\]       ??..(4)