Q 11-13-039JEE MainJEE Main 2026 (6 Apr, Shift 2)Medium
A spring stretches by $2$ mm when it is loaded with a mass of $200$ g. From equilibrium position the mass is further pulled down by $2$ mm and released. The frequency associated with the system and maxmimum energy in the spring are ______ Hz and ______ J, respectively. (Take $g = 10\ \text{m/s}^2$)
Answer: (A) $\dfrac{5\sqrt{50}}{\pi}$ and $8 \times 10^{-3}$
$k = \dfrac{mg}{x_0} = \dfrac{0.2 \times 10}{0.002} = 1000$ N/m.
$f = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}} = \dfrac{\sqrt{5000}}{2\pi} = \dfrac{10\sqrt{50}}{2\pi} = \dfrac{5\sqrt{50}}{\pi}$ Hz.
The largest stretch is $2 + 2 = 4$ mm, so the maximum energy stored in the spring is $\dfrac{1}{2} \times 1000 \times (0.004)^2 = 8 \times 10^{-3}$ J.
Solution by Sreeraj P, M.Sc Physics