A block of mass ' m ' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm⁻¹ for n = _________. Numerical answer type. Work it out, then open the answer.

Answer: 24. Speed halves, so KE becomes E/4; spring stores E - E/4 = 3E/4. 1/2k(0.25)² = 3E/4 ⇒ k/32 = 3E/4 k = 24E So n = 24.

A block of mass ' m ' (as shown in figure) moving with kinetic energy… | JEE Main 2022 (28 Jul, Shift 1)

Q12JEE Main 2022 · 28 JUL · SHIFT 1Medium

Spring & Elastic Energy

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

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 24

Speed halves, so KE becomes $E/4$ ; spring stores $E - \frac{E}{4} = \frac{3E}{4}$ .
$\frac{1}{2}k(0.25)^2 = \frac{3E}{4} \Rightarrow \frac{k}{32} = \frac{3E}{4}$
$k = 24E$
So $n = 24$ .

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