PYQ NEET- Work Energy And Power L-6

Question: Water falls from a height of $60 \mathrm{~m}$ at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a turbine. The losses due to frictional force are $10 %$ of the input energy. How much power is generated by the turbine? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$#

A) $7.0 \mathrm{~kW}$

B) $10.2 \mathrm{~kW}$

C) $8.1 \mathrm{~kW}$

D) $12.3 \mathrm{~kW}$

Answer: $8.1 \mathrm{~kW}$#

Solution:#

$E=m g h$

$\mathrm{P}_{\text {input }}=\frac{m g h}{t}$

$=\frac{15 \times 10 \times 60}{1}=9000=9 \mathrm{~kW}$

$10 %$ loss $=0.9 \times 10^3$

$P_{\text {output }}=9 \times 10^3-0.9 \times 10^3=8.1 \mathrm{~kW}$