Question

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

• A. $\sqrt{2}m/s$
• B. $2\sqrt{2}m/s$
• C. $2m/s$
• D. $4\sqrt{2}m/s$

Answer 1

The correct option is B $2\sqrt{2}m/s$

Let x be the extension in the spring when 2Kg mass leaves contact with ground

So, $kx=mg$

$x=\frac{mg}{k}$

$=\frac{1}{2}m$

Using conservation of energy

$mgx=\frac{v^{2}m}{2}+\frac{k{x}^2}{2}$

$v=\sqrt{2gx-\frac{k{x}^2}{m}}$

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

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

Therefore, the speed will be $2\sqrt{2}m/s$.