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A body of mass $1000 \mathrm{~kg}$ is moving horizontally with a velocity $50 \mathrm{~m} / \mathrm{s}$. A mass of $250 \mathrm{~kg}$ is added. Find the final velocity.
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Verified Answer
The correct answer is:
$40 \mathrm{~m} / \mathrm{s}$
Mass of the body, $m=1000 \mathrm{~kg}$
$$
v=50 \mathrm{~m} / \mathrm{s}
$$
After adding $250 \mathrm{~kg}$, new mass of the body,
$$
\begin{aligned}
m^{\prime} &=m+250 \\
&=1000+250 \\
&=1250 \mathrm{~kg}
\end{aligned}
$$
If $v^{\prime}$ be the final velocity of the body, then by conservation of linear momentum,
$$
\begin{aligned}
m v &=m^{\prime} v^{\prime} \\
\Rightarrow 1000 \times 50 &=1250 \times v^{\prime} \\
\Rightarrow \quad v^{\prime} &=\frac{1000 \times 50}{1250} \\
&=40 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
$$
v=50 \mathrm{~m} / \mathrm{s}
$$
After adding $250 \mathrm{~kg}$, new mass of the body,
$$
\begin{aligned}
m^{\prime} &=m+250 \\
&=1000+250 \\
&=1250 \mathrm{~kg}
\end{aligned}
$$
If $v^{\prime}$ be the final velocity of the body, then by conservation of linear momentum,
$$
\begin{aligned}
m v &=m^{\prime} v^{\prime} \\
\Rightarrow 1000 \times 50 &=1250 \times v^{\prime} \\
\Rightarrow \quad v^{\prime} &=\frac{1000 \times 50}{1250} \\
&=40 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
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