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.

One end of a 100 cm long rod is fixed. At its free end a screw is atta

1.	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.
Answer» SOLUTION :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)`