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A $30 \mathrm{~kg}$ boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is $10 \mathrm{~m}$ long and weighs $10 \mathrm{~kg}$.
If the boy walks to the near edge of the plank, how far from the shore does the plank move
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If the boy walks to the near edge of the plank, how far from the shore does the plank move
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Verified Answer
The correct answer is:
$7.5 \mathrm{~m}$
COM of system remains at same position in absence of any external force.
Position ( $x$-coordinate) of COM initially (taking origin at shore is)
$$
\begin{aligned}
x_{\mathrm{COM}} & =\frac{m_1 x_1+m_2 x_2}{m_1+m_2} \\
& =\frac{10 \times 5+30 \times 10}{10+30}=\frac{35}{4} \mathrm{~m}
\end{aligned}
$$
When boy changes his position, let the plank moves by distance $d$, then
$$
\begin{aligned}
& x_{\mathrm{COM}}=\frac{m_1 x_1^{\prime}+m_2 x_2^{\prime}}{m_1+m_2} \\
& \Rightarrow \frac{35}{4}=\frac{10(5+d)+30 d}{10+30} \Rightarrow 350=50+40 d \\
& \Rightarrow \frac{300}{40}=d \quad \Rightarrow d=7.5 \mathrm{~m} \\
&
\end{aligned}
$$
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