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
• B. 1 cm down
• C. 2 cm down
• D. 2 cm up

Answer 1

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 $1cm$

centre of mass = $\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$

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

$40=70+30y_2$

$y_2=-1$

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)