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Question
Two blocks of masses 10 kg and 20 kg are placed on the X-axis. The first mass is moved on the axis by a distance of 2 cm. By what distance should the second mass be moved to keep the position of the centre of mass unchanged?
Solution
Let the two masses m1 and m2 be placed on the X-axis.
It is given that:
m1 = 10 kg
m2 = 20 kg
The first mass is displaced by a distance of 2 cm.
\[\therefore X_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}\]
\[ \Rightarrow X_{cm} = \frac{10 \times 2 + 20 x_2}{30}\]
As the position of the centre of mass remains unchanged,
Xcm = 0
\[\Rightarrow 0 = \frac{20 + 20 x_2}{30}\]
\[ \Rightarrow 20 + 20 x_2 = 0\]
\[ \Rightarrow 20 = - 20 x_2 \]
\[ \Rightarrow x_2 = - 1\]
Therefore, to keep the position of centre of mass unchanged, the block of mass 20 kg should be moved by a distance of 1 cm, towards left.
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