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A thin - walled cylinder of mass (m), he...

A thin - walled cylinder of mass (m), height (h) and cross- sectional area (A) is filled with a gas and floats on the surface of water. As a result of leakage from the lower part of the cylinder, the depth of its submergence has increased by`Delta h`. Find the initial pressure `p_(1)` of the gas in the cylinder if the atmospheric pressure is `p_(0)` and the temperature remains constant.

Text Solution

Verified by Experts

The correct Answer is:
A, D
`p_2 =` pressure at depth `x`
(##DCP_V03_C20_E01_120_S01##).
`p_1 V_1 = p_2 V_2`
or `p_1 (Ah) = p_2(A)(h -Delta h)`
`:. p_1 = (p_2(h - Delta h))/(h)`
Initially, `mg = rho g x A`
Now, `p_2 = p_0 + rho g x = p_0 + (m g)/(A)`
Substituting in Eq. (i), we have
`p_1 = (p_0+(mg)/(A))(1 - (Delta h)/(h))`.
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