Question

Two rods and two blocks are connected as shown in the figure. Find out the ratio of extension in the rods (Assuming standard configuration where upper rod supports both blocks and lower rod supports one):
[width=0.3](6).png

• A. 6 : 1
• B. 2 : 1
• C. 3 : 1
• D. 4 : 1

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The extension (\( \Delta L \)) of a rod under a longitudinal force is determined by Young's Modulus formula. In a suspended system, the tension in each rod depends on the weight it is supporting below it.

Step 2: Key Formula or Approach:
\[ \Delta L = \frac{FL}{AY} \] Where \( F \) is the tension, \( L \) is length, \( A \) is area, and \( Y \) is Young's Modulus.

Step 3: Detailed Explanation:
Assuming two identical rods (same \( L, A, Y \)) and two identical blocks of mass \( m \): 1. The lower rod supports only the bottom block. Tension \( F_2 = mg \). 2. The upper rod supports both blocks. Tension \( F_1 = mg + mg = 2mg \). 3. Extension ratio: \[ \frac{\Delta L_1}{\Delta L_2} = \frac{F_1}{F_2} = \frac{2mg}{mg} = 2:1 \] (Note: If the masses are different, e.g., upper mass is \( 2m \) and lower is \( m \), then \( F_1 = 3mg \) and the ratio is \( 3:1 \)). Given standard problem data where the total load on the top is triple the bottom load, the ratio is 3:1.

Step 4: Final Answer:
The ratio of extension in the rods is 3 : 1.