System shown in figure is released from rest. Pulley and spring are massless and friction is absent

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5.Work, Energy, Power and Collision

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System shown in figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of $5\, kg$ block, when $2\, kg$ block leaves the contact with ground is : (take force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$)

A

$\sqrt 2\, m / s$

B

$2\sqrt 2 \,m/s$

C

$2 \,m/s$

D

$4\sqrt 2 \,m/s$

Solution

Let $x$ be the extension in the spring when 2 kg block leaves the contact with ground. Then,

$\mathrm{Kx}=2 \mathrm{g}$

$\text { or } \quad x=\frac{2 g}{K}=\frac{2 \times 10}{40}=\frac{1}{2} \mathrm{m}$

Now, from conservation of mechnical energy.

$\operatorname{mg} \mathrm{x}=\frac{1}{2} \mathrm{Kx}^{2}+\frac{1}{2} \mathrm{mv}^{2}$

$\mathrm{or}$ $v=\sqrt{2 g x-\frac{K x^{2}}{m}}$

$=\sqrt{2 \times 10 \times \frac{1}{2}-\frac{40}{4 \times 5}}$

$=2 \sqrt{2} \mathrm{m} / \mathrm{s}$

Standard 11

Physics

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