JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Elasticity & SHM

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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 of

A

B

is 2 and the ratio of their Young's moduli

(Y_{A} / Y_{B})

is 0.5 . The ratio of elongations in A to B is

____

(A)1
(B)4
(C)8
(D)6✓ Correct

Answer: (D)

Solution

String A carries both blocks, so its tension is

T_{A} = 3 M g

, while string B carries only the lower block,

T_{B} = 2 M g

. With elongation

Δ ℓ = \frac{T ℓ}{Y A}

and equal cross-sections,

\frac{Δ ℓ _{A}}{Δ ℓ _{B}} = \frac{T _{A}}{T _{B}} \cdot \frac{ℓ _{A}}{ℓ _{B}} \cdot \frac{Y _{B}}{Y _{A}} = \frac{3 M g}{2 M g} \times 2 \times \frac{1}{0.5} = \frac{3}{2} \times 2 \times 2.

The ratio of elongations of A to B is

6

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Elasticity & SHM

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