A ball of mass $4 \mathrm{~kg}$, moving with a velocity of $10 \mathrm{~ms}^{-1}$, collides with a spring of length $8 \mathrm{~m}$ and force constant $100 \mathrm{Nm}^{-1}$. The length of the compressed spring is $x \mathrm{~m}$. The value of $\mathrm{x}$, to the nearest integer, is
(6)
Let's say the compression in the spring by: $y$. So, by work energy theorem
we have
$\Rightarrow \frac{1}{2} \mathrm{mv}^{2}=\frac{1}{2} \mathrm{ky}^{2}$
$\Rightarrow \mathrm{y}=\sqrt{\frac{\mathrm{m}}{\mathrm{k}} \cdot \mathrm{v}}$
$\Rightarrow y=\sqrt{\frac{4}{100} \times 10}$
$\Rightarrow y=2 m$
$\Rightarrow$ final length of spring $=8-2=6 m$
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