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Question

Two blocks of masses 10 kg and 30 kg are placed along a vertical line. If the first block is raised through a height of 7 cm by what distance should the second mass be moved to raise the center of mass by 1 cm.


A
1 cm up
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B
1 cm down
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C
2 cm down
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D
2 cm up
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Solution

The correct option is B 1 cm down
  Two masses $$m_1$$  and $$m_2$$ are kept in verticle line 
   $$m_1=10kg$$                            $$m_2=30kg$$
   $$y_1=7cm$$                              $$y_2=?$$

The centre of mass raised by $$1 cm$$
 
 centre of mass = $$\dfrac{m_1 y_1+m_2 y_2}{m_1+m_2}$$

                      1  =  $$\dfrac{10\times 7+30\times y_2}{10+30}$$

                     $$40 = 70+30y_2$$
                     $$y_2 = -1$$
So, $$m_2=30kg$$ body should be displaced $$1cm$$ downward ,so as to raise the centre of mass through $$1cm$$

 so the correct answer  is (B)


Physics

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