A mass of $0.5 \mathrm{~kg}$ moving with a speed of $1.5 \mathrm{~m} / \mathrm{s}$ on a horizontal smooth…
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:
$0.15 \mathrm{~m}$
$0.12 \mathrm{~m}$
$1.5 \mathrm{~m}$
$0.5 \mathrm{~m}$
Solution
According to the question
$\begin{aligned}
\frac{1}{2} m v^2 & =\frac{1}{2} k x^2 \\
\Rightarrow \quad x & =v \sqrt{\frac{m}{k}}=1.5 \sqrt{\frac{0.5}{50}} \\
& =0.15 \mathrm{~m}
\end{aligned}$
