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)  0.4 cm        

B)  2.4 cm

C)  1.8 cm         

D)  1.2 cm

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 shifts to \[{{\text{O}}_{\text{2}}}\] at a distance \[{{x}_{2}}\]from original centre. The position of new centre of mass is given by \[{{X}_{CM}}=\frac{-\sigma .\pi {{b}^{2}}.{{x}_{1}}}{\sigma .\pi {{a}^{2}}-\sigma .\pi {{b}^{2}}}\] Here, \[a=6\,cm,\,b=2\,cm,{{x}_{1}}=3.2\,cm\] Hence,\[{{X}_{CM}}=\frac{-\sigma \times \pi {{(2)}^{2}}\times 3.2}{\sigma \times \pi \times {{(6)}^{2}}-\sigma \times \pi \times {{(2)}^{2}}}\] \[=\frac{12.8\,\pi }{32\,\pi }\] \[=-0.4\,cm\]