A block is hanged by means of two identical wires having cross section area 1`mm^(2)` as shown in the diagram. If temperature is lowered by `10^(@)C`, find the mass (in kg) to be added to the hanging mass such that the junction (J) remains at initial position, Given that coefficient of linear expansion `alpha=2xx10^(-5)//.^(@)C`, Young's modolus `Y=5xx10^(11) N//m^(2)` for the wire.

Options

A. 10
B. 12
C. 14
D. 16

Explanation

Change in tension =T
`2T sin 37^(@)-(Deltam)g`
`T=(Deltam)g`
`2sin 37^(@)`
But `Deltal=(TL)/(AY)=Lxx(Delta theta)`
`((Deltam)g)/(2 sin 37^(@))(1)/(AY)=alpha(Deltatheta)`
`therefore Deltam=12kg`