One end of a 100 cm long rod is fixed. At its free end a screw is attached and the pitch of the screw is 0.5 mm. The rod can move along its length on turning the screw. The screw has a circular scale with 100 divisions. It moves by one small scale division of 0.5 mm per turn. At `20^(@)C`, the pitch scale reads a little over zero and the circular scale reads 92. When the temperature is increased to `100^(@)C`, the pitch scale reading changes to a little above 4 divisions and the circular scale reading is 72. Find the coefficient of linear expansion of the material of the rod.

Explanation

Screw pitch = 0.5 mm and total number of circular scale divisions = 100
`therefore` Least count of screw
`" "="screw pitch"/"total no. of circular scale divisions"=0.5/100mm`
`therefore` The reading of the screw scale at `20^(@)C`
`" " =0 times 0.5+92 times 0.005=0.46mm,`
and the reading on that scale at `100^(@)C`
`" " =4 times 0.5+72 times 0.005=2.36mm`
`therefore` The linear expansion of the rod
`" "=2.36-0.46=1.9mm=0.19cm`
`therefore` Coefficient of linear expansion of the material of the rod
`" " =0.19/(100 times (100-20))=2.375 times 10^(-5@)C^(-1)`