A string A of length 0.314 m and Young's modulus $2\times {10}^{10}N/{m}^{2}$ is connected to another string B of length and Young's modulus both twice of those of A. this series combination of string is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg . The net change in length of the combination is _____ mm (radius of both the strings is 0.2 mm and acceleration due to gravity $=10m/{s}^{2})$
(Mass of both strings is to be neglected as compared to the mass of load)

[04 April, 2026 (Shift-I)]

Question

A string A of length 0.314 m and Young's modulus $2\times {10}^{10}N/{m}^{2}$ is connected to another string B of length and Young's modulus both twice of those of A. this series combination of string is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg . The net change in length of the combination is _____ mm (radius of both the strings is 0.2 mm and acceleration due to gravity $=10m/{s}^{2})$
(Mass of both strings is to be neglected as compared to the mass of load)

[04 April, 2026 (Shift-I)]

YESPYQ · Accepted Answer

Correct answer: b) 2. For string A : $L=l,Y=Y$ For string B : $L=2l,Y=2Y$ total extension is $\overset{^}{L}l=\overset{^}{L}{l}_{A}+\overset{^}{L}{l}_{g}$ $=\frac{\mathrm{m}g}{\mathrm{AV}}+\frac{\mathrm{m}(2n)}{\mathrm{A}(2\mathrm{V})}=\frac{2\mathrm{mg}}{\mathrm{AV}}$ $=\frac{2\times 0.8\times 10\times (0314)}{3.14\times {\left(2\times {10}^{-4}\right)}^{2}\times 2\times {10}^{10}}$ $\Delta l=2\times {10}^{-3}\mathrm{m}=2\mathrm{mm}$

A string A of length 0.314 m and Young's modulus \(2\times {10}^{10}N/{m}^{2}\) is connected to another string B of leng…

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