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Q.

A motor of power P₀ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the motor is increased to P₁. The ratio of P₁ to P₀ is :

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a

n² : 1

b

n : 1

c

n⁴ : 1

d

n³ : 1

answer is C.

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Detailed Solution

$r = \frac{V}{t} = Av$

$P = Fv$

$P = (\frac{m}{t}) v^{2} = (\frac{ρV}{t}) {(\frac{r}{A})}^{2} = \frac{{ρr}^{3}}{A^{2}}$

$P \propto r^{3}$
$P^{1} = n^{3} P$

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A motor of power P0 is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the motor is increased to P1. The ratio of P1 to P0 is :