A) 15.2 kg
B) 3.7 kg
C) zero
D) 7.5 kg
Correct Answer: D
Solution :
Initial mass of the gas \[{{m}_{1}}=1\,0\,kg\] Initial pressure \[{{P}_{1}}=10\,N\text{/}{{m}^{2}}\] Final pressure \[{{P}_{2}}=2.5\times {{10}^{6}}N\text{/}{{m}^{2}}\] According to kinetic theory of gases \[PV=\frac{1}{3}m{{c}^{-2}}\] or \[P\propto m\] Hence, \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\] or \[\frac{{{10}^{7}}}{2.5\times {{10}^{6}}}=\frac{10}{{{m}_{2}}}\] or \[{{m}_{2}}=2.5\,kg\] Hence, quantity of gas taken out from the cylinder is \[10-2.5=7.5\,kg\]
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