question_answer

In the situation shown in the figure, the system is in equilibrium. All the strings, spring and pulley are light. Just after cutting the string AB,

A) the tension in the string GH is 6 g

B) the tension in the string GH is zero                                                   

C) the tension in string GH is \[\frac{21}{4}g\]

D) the 2 kg block remains in equilibrium

Correct Answer: C

Solution :

[c]

In equilibrium, just before the string AB is cut the tension in spring is 5g.

Just after the string AB is cut the spring force won't change but all blocks except of 5 kg start accelerating.

Rough free body diagram is shown in figure.

\[a=\frac{\text{Net pulling force}}{\text{Total mass}}\]\[=\frac{5g+g-3g}{4}=\frac{3g}{4}\]

For 1 kg block (connected to spring)

Free body diagram would be as shown

\[5g+g-T=1\times \frac{3g}{4}\]

\[T=6g-\frac{3g}{4}=\frac{21}{g}\]