Work Energy Power

JEE Main level, single correct, medium

149 of 183

Question 149 of 183

The ratio of powers of two motors is 3xx+1,\dfrac{3\sqrt{x}}{\sqrt{x+1}}, that are capable of raising 300kg300kg water in 55 minutes and 50kg50kg water in 22 minutes respectively from a well of 100m100m deep. The value of xx will be

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Answer: (A) 1616

The work done in raising the water is W=mghW=mgh.
Power is P=WtP=\dfrac{W}{t}
Let the powers of both the motors be {P}_{1}&{P}_{2} respectively.
Hence, the ratio of the powers is,
P1P2=300×g×1005×6050×g×1002×60=6025⇒3xx+1=2.4\dfrac{{P}_{1}}{{P}_{2}}=\dfrac{\dfrac{300\times g\times 100}{5\times 60}}{\dfrac{50\times g\times 100}{2\times 60}}=\dfrac{60}{25} \Rightarrow \dfrac{3\sqrt{x}}{\sqrt{x}+1}=2.4
⇒3x=2.4x+2.4\Rightarrow 3\sqrt{x}=2.4\sqrt{x}+2.4
⇒x=16\Rightarrow x=16

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