A container of mass m is pulled by a constant force in which a second block of same mass m is placed

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5.Work, Energy, Power and Collision

hard

A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$. Initially the spring is in its natural length. Velocity of the container at the instant compression in spring is maximum for the first time :-

A

$\pi F\ \sqrt{\frac{1}{2km}}$

B

$\frac{\pi F}{2}\ \sqrt{\frac{1}{2km}}$

C

$\pi F\ \sqrt{\frac{1}{km}}$

D

$\frac{\pi F}{2}\ \sqrt{\frac{1}{km}}$

Solution

$\mathrm{Ft}=2 \mathrm{mv}(\mathrm{i})$

$\mathrm{t}=\frac{\mathrm{T}}{2}=\frac{2 \pi}{2} \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

$t=\pi \sqrt{\frac{m}{2 k}}$

$\mathrm{F} \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}=2 \mathrm{mv}$

$v=\frac{F \pi}{2} \sqrt{\frac{1}{2 k m}}$

Standard 11

Physics

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