Question
Two blocks of masses $10kg$ and $30kg$ are placed along a vertical line. The first block is raised through a height of $7cm$. By what distance should the second mass be moved to raise the centre of mass by $1cm$?
✓
Answer
Two masses $m_1$ & $m_2$ are kept in a vertical line.$m_1 = 10kg, m_2 = 30kg$
The first block is raised through a height of 7cm.
The centre of mass is raised by 1cm.
$\therefore1=\frac{\text{m}_1\text{y}_1+\text{m}_2\text{y}_2}{\text{m}_1+\text{m}_2}=\frac{10\times7+\text{30y}_2}{40}$
$\Rightarrow1=\frac{70+30\text{y}_2}{40}$
$\Rightarrow70+30\text{y}_2=40$
$\Rightarrow30\text{y}_2=-30$
$\Rightarrow\text{y}_2=-1$
The 30kg body should be displaced 1cm downward inorder to raise the centre of mass through 1cm.
The first block is raised through a height of 7cm.
The centre of mass is raised by 1cm.
$\therefore1=\frac{\text{m}_1\text{y}_1+\text{m}_2\text{y}_2}{\text{m}_1+\text{m}_2}=\frac{10\times7+\text{30y}_2}{40}$
$\Rightarrow1=\frac{70+30\text{y}_2}{40}$
$\Rightarrow70+30\text{y}_2=40$
$\Rightarrow30\text{y}_2=-30$
$\Rightarrow\text{y}_2=-1$
The 30kg body should be displaced 1cm downward inorder to raise the centre of mass through 1cm.
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