Question

A rod of mass \(m\) and length \(l\) is attached to two ideal strings. Find tension in the left string just after the right string is cut.

• A. \( \frac{mg}{2} \)
• B. \( \frac{mg}{4} \)
• C. \( \frac{2}{3} mg \)
• D. \( \frac{mg}{5} \)

Hint:

When solving for tension in dynamic systems, remember to consider both the gravitational and the rotational forces that act on the object.

Answer 1

The Correct Option is B

Step 1: Understanding the problem.
The rod is attached to two ideal strings, and we are asked to find the tension in the left string just after the right string is cut. When the right string is cut, the left string will experience the full gravitational force of the rod.
Step 2: Analyzing the forces.
Using the formula for angular acceleration \( \alpha = \frac{mg}{2l} \) when the right string is cut, we can find the tension.
\[ T = \frac{mg}{4} \] Thus, the tension in the left string is \( \frac{mg}{4} \).
Step 3: Conclusion.
The correct answer is (2) \( \frac{mg}{4} \), as calculated.