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Question
Two blocks of masses 10 kg and 30 kg are placed along a vertical line. The first block is raised through a height of 7 cm. By what distance should the second mass be moved to raise the centre of mass by 1 cm?
Solution
Let the two masses m1 and m2 are kept along a vertical line.
It is given that:
m1 = 10 kg
m2 = 30 kg
First block is raised through a height of 7 cm.
Thus, to raise the centre of mass by 1 cm:
\[\text{ Ycm }= \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2}\]
\[ \Rightarrow 1 = \frac{10 \times 7 + 30 \times y_2}{40}\]
\[ \Rightarrow 70 + 30 y_2 = 40\]
\[ \Rightarrow 30 y_2 = - 30\]
\[ \Rightarrow y_2 = - 1\]
Therefore, the 30 kg block (m2) should be moved by 1 cm downwards in order to raise the centre of mass by 1 cm.
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