A) 7.5 kg
B) 15.2 kg
C) 10.5 kg
D) none of these
Correct Answer: A
Solution :
Here: initial mass of the gas \[{{m}_{1}}=10kg\] Initial pressure \[{{P}_{1}}={{10}^{7}}N/{{m}^{2}}\] Final pressure \[{{P}_{2}}=2.5\times {{10}^{6}}N/{{m}^{2}}\] From kinetic theory of gases \[PV=\frac{1}{3}m{{c}^{2}}\] \[\Rightarrow \] \[P\propto m\] Hence, \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\] or \[\frac{{{10}^{7}}}{2.5\times {{10}^{6}}}=\frac{10}{{{m}^{2}}}\] \[\Rightarrow \] \[{{m}_{2}}=\frac{10}{4}=2.5\] The quantity of gas taken out \[=10-2.5=7.5kg\]
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