A ` 5 m` long cylindrical steel wire with radius ` 2xx10 ^(-3) m ` is suspended vertically from a rigid support and carries a bob of mass ` 100 kg ` at the other end . If the bob gets snapped , calculate the change in temperature of the wire ignorning radiation looses. ( Take ` g = 10 m//s ^(2) `)
( For the steel wire , young's modulus `= 2.1 xx10^(11) N//m^(2) ` , Density `= 7860 kg// m^(3) `, Specific heat `= 420 J/ kg -@ C` ) .

Answer

A, C, D

Explanation

`Delta l = (Fl)/AY `
` U = 1/2 K (Delta l ^(2)) `
`= (1/2(YA)/l)(Deltal^(2)) `
` 1/2 ((YA)/(l))((Fl)/(AY))^(2)`
` (F^(2)l)/(2 AY) = m S Delta theta `
`:. Delta theta = (F^(2)l)/(2AYms)`
`((Mg)^(2) l)/(2( pi r^(2))Y(l pi r^(2)) rhos)`
`= (M^(2) g^(2))/(2 pi.^(2)r^(4)Yrhos)`
` ((100xx9.8)^(2))/(2pi^(2)(2xx10.^(-3)).^(4) ( 2.1 xx10.^(11))( 7860)(420))`
` ~~ 4.568xx10^(-3).^@C`