A ball of mass 4 kg,


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



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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