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A mass of $0.5 \mathrm{~kg}$ moving with a speed of $1.5 \mathrm{~m} / \mathrm{s}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50 \mathrm{~N} / \mathrm{m}$. The maximum compression of the spring would be:
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Verified Answer
The correct answer is:
$0.15 \mathrm{~m}$
According to the question
$$
\begin{aligned}
\frac{1}{2} m v^2 & =\frac{1}{2} k x^2 \\
\Rightarrow \quad x & =v \sqrt{\frac{m}{k}}=1.5 \sqrt{\frac{0.5}{50}} \\
& =0.15 \mathrm{~m}
\end{aligned}
$$
$$
\begin{aligned}
\frac{1}{2} m v^2 & =\frac{1}{2} k x^2 \\
\Rightarrow \quad x & =v \sqrt{\frac{m}{k}}=1.5 \sqrt{\frac{0.5}{50}} \\
& =0.15 \mathrm{~m}
\end{aligned}
$$
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