A wire having cross-sectional area S is attatched to wall on one side and a block of mass M on the other side which placed on a horizontal surface having coefficient of friction `mu` as shown . Material of wire has coefficient of thermal expansion `alpha` and Young's modulus Y. At initial temperature there is no stress in the wire. Now the wire is cooled. At what decrease in temperature the block will begin to move.

Options

A. `(muMg)/(alphaYS)`
B. `(2muMg)/(alphaYS)`
C. `(muMg)/(2alpha YS)`
D. none

Answer

A

Explanation

On decreasing, the temperature by `(Deltatheta)`, the tension developed will be
`T=Y Salpha(Deltatheta)`
when about to ship, `T=f_(max)`
`Ysalpha(Delta theta) =muMg`
`Deltatheta=(mu Mg)/(alphaYS)`