Question

A block of mass ' $m$ ' (as shown in figure) moving with kinetic energy E compresses a spring through a distance $25cm$ when, its speed is halved. The value of spring constant of used spring will be $nEN{m}^{-1}$ for $n=$ ___

Answer 1

Answer: 24

Using work - energy theorem
$W_{\text{ net }}=\left(K_f-K_i\right)$
$\Rightarrow -\frac{1}{2}K{x}^2=\frac{1}{2}m{\left(\frac{v}{2}\right)}^2-\frac{1}{2}m{v}^2=\frac{E}{4}-E$
$\Rightarrow \frac{1}{2}K{x}^2=\frac{3E}{4}\Rightarrow K=\frac{3E}{2x^2}$
$\Rightarrow K=\frac{3E}{2\times {\left(\frac{1}{4}\right)}^2}=24E$
$n=24$