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A gas filled freely collapsible balloon is pushed from the surface level of lake to a depth of 100 metre . Calculate what per cent of its original volume , the balloon finally have ? Assume ideal gas nature .

$(a)\;9\% \;of\; V_i\qquad(b)\;9.37\% \;of\; V_i\qquad(c)\;0.93\% \;of\; V_i\qquad(d)\;10\% \;of\; V_i$

1 Answer

Pressure at 100 metre depth
= Atmospheric pressure + pressure of water
= $76\times13.6\times981 + 100\times100\times1\times981$
= 1013961.6 + 9810000
$= 10823961.6 \;dyne\;cm^{-2}$
Let volume of balloon at the surface level be $V_i \;cm^3$ and the volume of balloon at the depth of 100 metre is $V_f$ then
$P_1V_1 = P_2V_2$
$\therefore 76\times13.6\times981\times V_i = 10823961.6\times V_f$
$V_f = \large\frac{76\times13.6\times981}{10823961}\times V_i$
$V_f = 0.0937 V_i$
$V_f = 9.37 \%\; of\; V_i$
Hence answer is (B)
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