Q 11-05-133JEE MainJEE Main 2022 (28 Jul, Shift 1)Easy
A block of mass $m$, sliding on a smooth horizontal surface with kinetic energy $E$, hits a spring fixed to a wall and compresses it through a distance $25$ cm when its speed is halved. The value of spring constant of used spring will be $nE\ \text{N m}^{-1}$ for $n$ = ______ .
Numerical value type. Enter your answer.
Answer: 24
When the speed is halved, the kinetic energy is $\dfrac E4$, so the spring has stored $\dfrac{3E}{4}$:
$$\frac12k(0.25)^2 = \frac{3E}{4} \Rightarrow k = \frac{3E}{2\times0.0625} = 24E$$
$n = 24$.
Solution by Sreeraj P, M.Sc Physics