A) \[n:1~\]
B) \[{{n}^{2}}:1\]
C) \[{{n}^{3}}:1\]
D) \[{{n}^{4}}:1\]
Correct Answer: A
Solution :
Power of motor initially \[={{P}_{0}}\] Let, rate of flow of motor \[=(x)\] Since, power, \[{{P}_{0}}=\frac{work}{time}=\frac{mgy}{t}\] \[=mg\left( \frac{y}{t} \right),\] \[\frac{y}{t}=x=\]rate of flow of water \[=mgx\] ...(i) If rate of flow of water is increased by n times, ie, (nx). Increased power \[{{P}_{1}}=\frac{mgy}{t}\] \[=mg\left( \frac{y}{t} \right)\] \[=mgn.x\] \[=nmgx\] ?..(ii) The ratio of power \[\frac{{{P}_{1}}}{{{P}_{0}}}=\frac{nmgx}{mgx}\] \[\frac{{{P}_{1}}}{{{p}_{0}}}=\frac{n}{1}\] \[\Rightarrow \] \[{{P}_{1}}:{{P}_{0}}=n:1\]
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