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JEE Main 2022 (25 Jun, Shift 1) · Spring & Elastic Energy

Spring & Elastic Energy question from JEE Main 2022 (25 Jun, Shift 1)

Q13JEE Main 2022 · 25 JUN · SHIFT 1Medium

Spring & Elastic Energy

A 0.5 kg block moving at a speed of 12 ms ${}^{-1}$ compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _______________ Nm ${}^{-1}$ .

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

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Answer: 600

Initial KE $= \frac{1}{2}(0.5)(12^2) = 36$ J; at half speed KE $= 9$ J.
Spring PE $= 36 - 9 = 27$ J $= \frac{1}{2}k(0.3)^2$
$k = \frac{54}{0.09} = 600$
So $k = 600\ \text{N m}^{-1}$ .

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