The pressure gauge shown in figure has a spring for which `k=60N//m` and the area of the piston is `0.50cm^(2)`. Its right end is connected to a closed container of gas at a gauge pressure of `30kPa`. How far will the spring be compressed if the region containing the spring is (a) in vacuum and (b) open to the atmosphere? Atmospheric pressure is `101kPa`.

Answer

A, B, C

Explanation

(a) Force from left hand side
=force from right hand side
`:. Kx=DeltapA`
`or, x=((Delta p)A)/k`
`=((30+101)xx10^(3)xx0.5xx10^(-4))/(60)`
`=0.109m or 10.9 cm`
(b) `x=((Delta p)A)/(k)`
`=(30xx10^(3)xx0.5xx10^(-4))/(60)`
`=0.025m` or `2.5 cm`.