A) \[n-\]times
B) \[{{n}^{2}}-\] times
C) \[{{n}^{3}}-\]times
D) \[{{n}^{4}}-\]times
Correct Answer: C
Solution :
If the motor pumps water (density \[=\rho \]) continuously through a pipe of area of cross- section A with velocity \[v,\]then mass flowing out per second. \[m=Av\rho \] ?(i) Rate of increase of kinetic energy \[=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}(Av\rho ){{v}^{2}}\] ?(ii) Mass \[m,\]flowing out per sec, can be increased to \[m\]by increasing \[v\]to \[v,\]then power increases from P to\[P.\] \[\frac{P}{P}=\frac{\frac{1}{2}A\rho v{{}^{3}}}{\frac{1}{2}A\rho {{v}^{3}}}or\frac{P}{P}={{\left( \frac{v}{v} \right)}^{3}}\] Now, \[\frac{m}{m}=\frac{A\rho v}{A\rho v}=\frac{v}{v}\] As \[m=nm,v=nv\] \[\therefore \] \[\frac{P}{P}={{n}^{3}}\Rightarrow P{{n}^{3}}P\]
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