question_answer

A small disc of radius 2 cm is cut from a disc of radius 6 cm, if the distance between their centers is 3.2 cm, what is 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 \[{{X}_{CM}}=\frac{-\sigma .\,\pi {{b}^{2}}.\,{{x}_{1}}}{\sigma .\,\pi {{a}^{2}}-\sigma \,.\,\pi {{b}^{2}}}\] Here, \[a=6\,cm,\,b=2\,cm,\,{{x}_{1}}=3.2\,cm\] Hence, \[{{X}_{CM}}=\frac{-\sigma \times \pi {{(2)}^{2}}\times 3.2}{\sigma \times \pi \times {{(6)}^{2}}-\sigma \times \pi \times {{(2)}^{2}}}\] \[=-\frac{12.8}{32\,\pi }\] = - 0.4 cm