A one kg block moves towards a light spring with a velocity of 8, m/s . When spring is com

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5.Work, Energy, Power and Collision

hard

A one kg block moves towards a light spring with a velocity of $8\, m/s$. When the spring is compressed by $3\, m$, its momentum becomes half of the original momentum. Spring constant of the spring is :-

A

$18/3\, N/m$

B

$16/3\, N/m$

C

$3\, N/m$

D

$8\, N/m$

Solution

$\frac{1}{2} m v_{1}^{2}-\frac{1}{2} m v_{2}^{2}=\frac{1}{2} k x^{2}$

$P_{1}^{2}-P_{2}^{2}=m k x^{2}$

$\frac{3}{4} \mathrm{P}_{1}^{2}=\mathrm{mkx}^{2}$

$\frac{3}{4} \mathrm{m}^{2} \mathrm{v}^{2}=\mathrm{m} \mathrm{k} \mathrm{x}^{2}$

$\mathrm{k}=\frac{3}{4} \times 1 \times \frac{64}{9}=\frac{16}{3} \mathrm{N} / \mathrm{m}$

Standard 11

Physics

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