A ball of mass 4, kg , moving with a velocity of 10, ms ^{-1} , collides with a spring of length 8,

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5.Work, Energy, Power and Collision

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A ball of mass $4\, kg$, moving with a velocity of $10\, ms ^{-1}$, collides with a spring of length $8\, m$ and force constant $100\, Nm ^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$, to the nearest integer, is ........ .

A

$4$

B

$9$

C

$6$

D

$12$

(JEE MAIN-2021)

Solution

Let's say the compression in the spring by: $y$.

So, by work energy theorem we have

$\Rightarrow \frac{1}{2} mv ^{2}=\frac{1}{2} ky ^{2}$

$\Rightarrow y =\sqrt{\frac{ m }{ k }} \cdot v$

$\Rightarrow y=\sqrt{\frac{4}{100}} \times 10$

$\Rightarrow y =2\, m$

$\Rightarrow$ final length of spring $=8-2=6\, m$

Standard 11

Physics

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