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An inverted bell lying at the bottom of ...

An inverted bell lying at the bottom of a lake `47.6 m` deep has `50 cm^3` of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure `= 70 cm` of `Hg` and density of `Hg = 13.6 g//cm^3`).

A

`350 cm^(3)`

B

`300 cm^(3)`

C

`250 cm^(3)`

D

`22 cm^(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
According to Boyle's law, pressure and volume are inversely proportional to each other i.e `P prop (1)/(V)`
`implies P_(1)V_(1) = P_(2)V_(2)`
`implies (P_(0)+hrho_(w)g)V_(1) = P_(0) V_(2)`
`implies V_(2)=(1+(hrho_(w)g)/(P_(0)))V_(1)`
`implies V_(2) (1+(47.6xx10^(2)xx1xx1000)/(70xx13.6xx1000))V_(1)`
`implies ["As" P_(2) = P_(0) = 70 "cm of Hg" = 70xx13.6xx1000]`
`implies V_(2) = (1+5)50cm^(3) = 300 cm^(3)`.
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