Question

Two particles of masses $m$ and $2m$ are connected by a string of length $L$ and placed at rest over a smooth horizontal surface. The particles are then given velocities as indicated in the figure shown. The tension developed in the string will be

• A. $\frac{m v^{2}}{2 L}$
• B. $\frac{3 m v^{2}}{4 L}$
• C. $\frac{4 m v^{2}}{3 L}$
• D. $\frac{8 m v^{2}}{3 L}$

Answer 1

Answer: (D)

$V_{c}=\frac{2 m v - m v}{\left(\right. 2 m + m \left.\right)}=\frac{v}{3}$
$V_{r e l}=v-\frac{v}{3}=\left(\frac{2 v}{3}\right)$
$r_{1}=\frac{m L}{3 m}=\frac{L}{3}$
$\therefore \, \, T=\frac{\left(2 m\right) \times \left(\frac{2 v}{3}\right)^{2}}{\left(\frac{L}{3}\right)}=\frac{8 m v^{2}}{3 L}$