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) 0.4cm                                   

B) 2.4cm                   

C) 1.8cm                   

D)        1.2cm

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 \[{{O}_{2}}\] 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, \[{{X}_{CM}}=\frac{-\,\sigma \times \pi {{(2)}^{2}}\times 3.2}{\sigma \times \pi \times {{(6)}^{2}}-\sigma \times \pi \times {{(2)}^{2}}}\]        \[=\frac{12.8\pi }{32\pi }\]        \[=-\,0.4\,cm\]