Question 117 of 183

A block of mass $m,$ lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k.$ The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F,$ the maximum speed of the block is:

A$\dfrac{F}{\sqrt{mk}}$B$\dfrac{2F}{\sqrt{mk}}$C$\dfrac{\pi F}{\sqrt{mk}}$D$\dfrac{F}{\pi \sqrt{mk}}$

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Answer: (A) $\dfrac{F}{\sqrt{mk}}$

When block attains maximum speed net force on $m$ is zero. $∴F=kx$

Or $x=\dfrac{F}{k}$

From work energy theorem

$-\dfrac{1}{2}k{\left(\dfrac{F}{k}\right)}^{2}+F\left(\dfrac{F}{k}\right)=\dfrac{1}{2}m{V}_{max}^{2}$

$\dfrac{{F}^{2}}{2k}=\dfrac{1}{2}m{V}_{max}^{2}$

${V}_{max}=\sqrt{\dfrac{F}{km}}$