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 ?

Answer 1

Two masses $m_1$ and $m_2$ are kept in a vertical line,

$m_1=10kg,m_2=30kg$

The first block is resied through a height of 7 cm.

The centre of mass is raised by 1 cm.

$\therefore 1=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$

$=\frac{10\times 7+30\times y_2}{40}$

$=\frac{70+30\times y_2}{40}$

$\Rightarrow 70+30\times y_2=0$

$\Rightarrow 30\times y_2=-30$

$\Rightarrow y_2=-1$

The 30 kg body should be displaced 1 cm downward in order to raise the centre of mass through 1 cm.