A ball of mass 4 kg , moving with a velocity of 10 m s - 1 , collides with a spring of length 8 m and force constant 100 N m - 1 . The length of the compressed spring is x m . The value of x , to the

Question

A ball of mass 4 kg , moving with a velocity of 10 m s - 1 , collides with a spring of length 8 m and force constant 100 N m - 1 . The length of the compressed spring is x m . The value of x , to the nearest integer, is ___ .

TestHub · Accepted Answer

Let's say the compression in the spring by: $y$ . So, by work-energy theorem we have

$\Rightarrow \frac{1}{2} m v^{2} = \frac{1}{2} k y^{2}$ $\Rightarrow y = \sqrt{\frac{m}{k}} \cdot v$ $\Rightarrow y = \sqrt{\frac{4}{100}} \times 10$ $\Rightarrow y = 2 m$

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

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