question_answer

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

A) \[40\]                                   

B) \[80\]

C)  \[50\]                                  

D)  \[0.01\]

Correct Answer: A

Solution :

The situation can be shown as: Let radius of complete disc is \[a\] and that of small disc is\[b\]. Also let centre of mass now shirts to\[{{O}_{2}}\] at a distance \[{{x}_{2}}\] from original centre. The position of new centre of mass is given by                 \[{{X}_{CM}}=\frac{-\sigma \cdot \pi {{b}^{2}}\cdot {{x}_{1}}}{\sigma \cdot \pi {{a}^{2}}-\sigma \cdot \pi {{b}^{2}}}\] Here,\[a=6\,\,cm,\,\,b=2\,\,cm,\,\,{{x}_{1}}=3.2\,\,cm\] Hence,\[{{X}_{CM}}=\frac{-\sigma \times \pi {{(2)}^{2}}\times 3.2}{\sigma \times \pi \times {{(6)}^{2}}-\sigma \times \pi \times {{(2)}^{2}}}\]                       \[=\frac{12.8\pi }{32\pi }\]                       \[=-0.4\,\,cm\]