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 ?

Given,

${\mathrm{m}}_1=10\mathrm{kg}, {\mathrm{m}}_2=30\mathrm{kg}, {\mathrm{y}}_1=7\mathrm{cm}, {\mathrm{y}}_2=?$

We know that,

$\mathrm{centre} \mathrm{of} \mathrm{mass} = \frac{{\mathrm{m}}_1{\mathrm{y}}_1+30\times {\mathrm{y}}_2}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

$1=\frac{10\times 7+30\times {\mathrm{y}}_2}{10+30}$

$40=70+30{\mathrm{y}}_2$

${\mathrm{y}}_2=-1$

So, $m_2$= 30kg body should be moved 1 cm downward in order for a 1 cm uplift in the centre of mass.