Question

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

• A. $\sqrt{3}m/s$
• B. $2\sqrt{2}m/s$
• C. $2m/s$
• D. $\sqrt{2}m/s$

Answer 1

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

$kx=2g$

$x=\frac{2g}{k}=\frac{2\times 10}{40}=\frac{1}{2}m$

by law of conservation of energy,

$mgx=\frac{1}{2}{k}^2+\frac{1}{2}m{v}^2$

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

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

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