# Mechanical Properties of Matter

**Question**

Find the rise in temperature of cable due to increased strain.

Properties of cable: !!alpha= 10^-5 //^0C!!, Young's modulus!!=10^11 \N//m^2!!

and cross sectional area !!= 3 \ cm^2!!

a) !!1.8 \ ^0C!!

b) !!2.0 \ ^0 C!!

c) !!2.4 \ ^0C!!

d) !!2.7 \ ^0C!!

**Solution**

Young's modulus, !!Y = (F//A)/((DeltaL)//L)!!

According to question !!T-mg=ma!!, where !!m!! is the weight of man.

Therefore, !!(DeltaL)/L= (m(g+a))/(AY)= 2.4xx10^-5 ....(1)!!

Strain !!= alpha DeltaT= (DeltaL)/L!!

From equation !!(1)!!, we get

!!DeltaT = 2.4 \ ^0C!!