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A block of mass 'm' moving with a speed ' $\large \upsilon$ ' compresses a spring through a distance 'x' before its speed reduces by 25%. The spring constant of the spring is

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\large \frac{{m{\upsilon ^2}}}{{4{x^2}}}

\large \frac{{3m{\upsilon ^2}}}{{4{x^2}}}

\large \frac{{7m{\upsilon ^2}}}{{16{x^2}}}

$\large \frac{{9m{\upsilon ^2}}}{{16{x^2}}}$

answer is C.

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Detailed Solution

$\frac{1}{2}k{x^2} = \frac{1}{2}m\left( {1 - \frac{9}{{16}}} \right){\upsilon ^2}$
$k{x^2} = m\frac{{7{\upsilon ^2}}}{{16}} \Rightarrow k = \frac{{7m{\upsilon ^2}}}{{16{x^2}}}$

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