Question

A person decides to use his bath tub water to generate electric power to run a 40 W bulb. The bath tub is located at a height of h m from ground an it holds V litres of water. He installs a water driven wheel generator on ground. The rate at which water should drain from bath tub to light the bulb if efficiency of machine be 90% is

• A. $\frac{11.11}{\rho gh}$
• B. 44.44 ρgh
• C. $\frac{44.44}{\rho gh}$
• D. $\frac{22.22}{\rho gh}$

Answer 1

Answer: (C)

$\frac{44.44}{\rho gh}$

Answer 2

Power = P= $\frac{dW}{dt} = \frac{d}{dt}$ (mgh) = $\frac{dV\rho gh}{dt}$

or P = $\frac{dV\rho gh}{dt}$ = $\rho dh\frac{dV}{dt}$

Since η =$\frac{P_{output}}{P_{input}}$

∴ P_output = η P_input = ηρgh$\frac{dV}{dt}$

or $\frac{dV}{dt}\eta\frac{P_{output}}{\eta\rho gh^{2}}$

= $\frac{40}{0.9}\rho gh = \frac{44.44}{\rho gh}$