A block of mass m is pushed against a spring whose spring constant is k fixed at one end with a wall

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5.Work, Energy, Power and Collision

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A block of mass $m$ is pushed against a spring whose spring constant is $k$ fixed at one end with a wall. The block can slide on a frictionless table as shown in figure. If the natural length of spring is $L_0$ and it is compressed to half its length when the block is released, find the velocity of the block, when the spring has natural length

A

$\sqrt {\frac{m}{k}} .\frac{{{L_0}}}{2}$

B

$\sqrt {\frac{k}{m}} .\frac{{{L_0}}}{2}$

C

$\sqrt {\frac{k}{m}} .{L_0}$

D

$\sqrt {\frac{{k{L_0}}}{m}} $

Solution

The energy stored in the spring when it is compressed to $\frac{\mathrm{L}_{0}}{2}$ is converted into kinetic energy of the block

$\frac{1}{2} m u^{2}=\frac{1}{2} k\left(\frac{L_{0}}{2}\right)^{2}$

Standard 11

Physics

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