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 ?

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Solution

Two masses $m_{1}$ & $m_{2}$ are placed on the X-axis $m_{1} = 10 k g, m_{2} = 30 k g$ .
The first block is raised through a height of $7 c m .$
The centre of mass is raised by $1 c m .$

$∴ 1 = \frac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}} = \frac{10 \times 7 + 30 y_{2}}{40}$

$\Rightarrow 1 = \frac{70 + 30 y_{2}}{40} \Rightarrow 70 + 30 y_{2} = 40 \Rightarrow 30 y_{2} = - 30 \Rightarrow y_{2} = - 1$

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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 ?

Two masses m1 & m2 are placed on the X-axis m1=10kg,m2=30kg. The first block is raised through a height of 7cm.The centre of mass is raised by 1cm.∴1=m1y1+m2y2m1+m2=10×7+30y240⇒1=70+30y240⇒70+30y2=40⇒30y2=−30⇒y2=−1