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# Power required to raise $300 liters$ of water per minute through a height of 6m using a pipe of diameter 2.4 cm is $(g=10 m/s^2)$

$\begin {array} {1 1} (a)\;600\;walt \\ (b)\;400\;walt \\ (c)\;1000\;walt \\ (d)\;2000\;walt \end {array}$

$W_1$= Work done against gravity $=mgh$
$\qquad=V \rho gh$
Work done against pressure difference
$W_2=\Delta PV= h \rho gV$
Total work done $=W_1 +W_2$
$\qquad= 2h \rho gV$
$P= \large\frac{W}{t}$
$\quad= \large\frac{2 \times 6 \times 10^3 \times 10 \times 300 \times 10^{-3}}{60}$
$\quad= 600\; walt$
Hence a is the correct answer.

edited Feb 18, 2014 by meena.p