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A small body having mass 1kg is rotating in a circle of radius 10cm. It is connected to the centre with the help of a string having young’s modulus = 10^11N/m^2. Find change in length of wire while the mass is rotating with constant speed of 2m/s. The cross sectional area of string is 1cm^2.

(a) 0.4μm

(b) 4μm

(c) 40μm

(d) 0.4m

This question was addressed to me in semester exam.

My question is based upon Solids Mechanical Properties in chapter Mechanical Properties of Solids of Physics – Class 11

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The correct choice is (a) 0.4μm

Explanation: Tension ‘T’ in string will be given by T = mv^2/R = 1*4/0.1 = 40N.

Stress = Y*Strain, where Y is young’s modulus. T/A=Y*ΔL/L

∴ ΔL = TL/AY = (40*0.1)/(0.0001*10^11)

= 4*10^-7m = 0.4μm.

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