PHYSICS A metal rod of cross-sectional area 10^{–4} m^{2}is hanging in a chamber kept at 20°C with a weight attached to its free end. The coefficient of thermal expansion of the rod is 2.5 × 10^{–6} K^{–1} and its Young's modulus is 4 ×10^{12} N/m^{2}. When the temperature of the chamber is lowered to T then a weight of 5000 N needs to be attached to the rod so that its length is unchanged. Then T is

KVPY 2019 SB SX Exam Previous Papers

Question : 91 of 120

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PHYSICS

A metal rod of cross-sectional area 10

^{–4}

^{2}

is hanging in a chamber kept at 20°C with a weight attached to its free end. The coefficient of thermal expansion of the rod is 2.5 × 10

^{–6}

^{–1}

and its Young's modulus is 4 ×10

^{12}

N/m

^{2}

. When the temperature of the chamber is lowered to T then a weight of 5000 N needs to be attached to the rod so that its length is unchanged. Then T is

15°C
12°C
5 °C
0°C

Validate

Solution:

{∆l}/l=α∆θ=F/{yA}

∆θ=F/{yAα}=5°C

∆θ20 – T = 5

T = 15°C

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