Two marks on a glass rod `10 cm` apart are found to increase their distance by `0.08 mm` when the rod is heated from `0^@ C "to" 100^@ C`. A flask made of the same glass as that of rod measures a volume of `100 cc at 0^@ C`. The volume it measures at `100^@ C` in (cc) is.

Options

A. 1002.4
B. 1004.2
C. 1006.4
D. 1008.2

Answer

A

Explanation

`gamma =(V_(2)-V_(1))/(V_(1)(T_(2)-T_(1))), alpha=(l_(2)-l_(1))/(l_(1)(T_(2)-T_(1)))`
`T_(1)=0^(@)C, T_(2)=100^(@)C`
`gamma=(V_(2)-V_(1))/(100V_(1)), alpha=(l_(2)-l_(1))/(100l_(1))`
`l_(1)=10cm, l_(2)-l_(1)=0.08mm= 0.008cm`
`alpha=(0.008)/(10xx100)=8xx10^(-6)//""^(@)C, gamma=3alpha=24xx10^(-6)//""^(@)C`
`therefore 24xx10^(-6)=(V_(2)-1000)/(1000xx 100)`
`V_(2)-1000=24xx10^(-6)xx10^(5)=2.4 therefore V_(2)=1002.4`cc