A load of 31.4 kg is suspended from a wire of radius 10^(-3)m and density 9xx10^(3)kg//m^(3). Calculate the change in temperature of the wire if 75% of the work done is converted into heat. The Young.s modulus and heat capacity of the material of the wire are 9.8 x10^(10) N//m^(2) and 490 J/kg K respectively.

A load of 31.4 kg is suspended from a wire of radius 10^(-3)m and dens

1.	A load of 31.4 kg is suspended from a wire of radius 10^(-3)m and density 9xx10^(3)kg//m^(3). Calculate the change in temperature of the wire if 75% of the work done is converted into heat. The Young.s modulus and heat capacity of the material of the wire are 9.8 x10^(10) N//m^(2) and 490 J/kg K respectively.
Answer» Solution :As work done in stretching an elastic BODY per unit volume is given by `(W)/(V)=(1)/(2) "stress" xx "strain" =(1)/(2) ("stress")/(Y)[ as Y=("stress")/("strain")]` `So W=(1)/(2)[(Mg)/(A)]^(2)(V)/(Y)[ "as stress" =(F)/(A)=(Mg)/(A)]` Now according to given Problem `H=(75//100)W` `ms DELTA theta=(3)/(4)xx(1)/(2)[Mg)/(pir^(2))](V)/(Y)(or) (rho V) s Delta theta=(3)/(4)xx(1)/(2) [(mg)/(pi^(2))]^(2) (V)/(Y)` `:. Delta theta=(3)/(8)[(31.4xx9.8)/(pixx10^(-6))]^(2)(1)/(9.8xx10^(10))xx(1)/(9XX10^(3)xx490)` `i.e, Delta theta=(1)/(120)K=8.33 xx10^(-3)K`