Question

Two unequal masses are connected on two sides of light string passing over a light and smooth pulley a shown in the figure. The system is released from rest. The larger mass is stopped $1$ sec after the system is set into motion and then released. Then The time elapsed before the string is tight again ($g=10m/{sec}^2$)

• A. $\frac{1}{4}$ sec
• B. $\frac{1}{2}$ sec
• C. $\frac{2}{3}$ sec
• D. $\frac{1}{3}$ sec

Answer 1

The correct option is D $\frac{1}{3}$ sec

The acceleration of the system.

$a=\frac{\left(M_1-M_2\right)g}{M_1+M_2}$

$a=\frac{g}{3}$

Velocity of $1kg$ box.

$\begin{array}{c}{v}_1=u+at\\ v_1=0+\frac{g}{3}\times 1\\ v_1=\frac{g}{3}\end{array}$

The displacement of both boxes are equal in magnitude.

$\begin{array}{c}\frac{gt}{3}-\left(\frac{1}{2}\right)g{t}^2=\left(\frac{1}{2}\right)g{t}^2\\ t=\frac{1}{3}\sec \end{array}$

Hence, Option $D$ is the correct answer.