Physics Q31 – JEE-MAIN 2026

Home Physics Mechanical Properties of SolidsQuestion #284

A metal string

A

is suspended from a rigid support and its free end is attached to a block of mass

M

. Second block having mass

2 M

is suspended at the bottom of the first block using a string

B

. The area of cross sections of strings

A

and

B

are same. The ratio of lengths of strings

A

B

2

and the ratio of their Young's moduli (

Y_{A} / Y_{B}

) is

0.5

. The ratio of elongations in

A

B

is _______.

Clue 1 of 3: Understand the forces

Identify the total force acting on each string due to the suspended masses.

🧠 Full Solution Path

Step 1: Determine the forces on each string✦ Active

String A supports both blocks, so the total force on string A is $F_{A} = (M + 2 M) g = 3 M g$ .

String B supports only the lower block, so the force on string B is $F_{B} = 2 M g$ .

Step 2: Recall the formula for elongation○ Expand

The elongation $Δ L$ of a string is given by the formula derived from Young's Modulus: $Δ L = \frac{F L}{A Y}$ , where $F$ is the force, $L$ is the original length, $A$ is the cross-sectional area, and $Y$ is Young's modulus.

Step 3: Calculate the ratio of elongations○ Expand

For string A, $Δ L_{A} = \frac{F_{A} L_{A}}{A_{A} Y_{A}} = \frac{3 M g \cdot L_{A}}{A \cdot Y_{A}}$ (since $A_{A} = A$ ). For string B, $Δ L_{B} = \frac{F_{B} L_{B}}{A_{B} Y_{B}} = \frac{2 M g \cdot L_{B}}{A \cdot Y_{B}}$ (since $A_{B} = A$ ). The ratio of elongations is:

\frac{Δ L_{A}}{Δ L_{B}} = \frac{\frac{3 M g \cdot L_{A}}{A \cdot Y_{A}}}{\frac{2 M g \cdot L_{B}}{A \cdot Y_{B}}} = \frac{3}{2} \cdot \frac{L_{A}}{L_{B}} \cdot \frac{Y_{B}}{Y_{A}}

Given $L_{A} / L_{B} = 2$ and $Y_{A} / Y_{B} = 0.5$ . From $Y_{A} / Y_{B} = 0.5$ , we get $Y_{B} / Y_{A} = 1 / 0.5 = 2$ . Substituting these values:

\frac{Δ L_{A}}{Δ L_{B}} = \frac{3}{2} \cdot (2) \cdot (2) = 6

Thus, the ratio of elongations in A to B is 6.

💡 Teacher's Secret Hint

Ensure correct identification of forces for each string and careful substitution of ratios.

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Physics Question 31 – JEE-MAIN 2026

Clue 1 of 3: Understand the forces

🧠 Full Solution Path