Question

An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60% . If $g = 10ms^{- 2}$, the power of the engine is

• A. $3.3kW$
• B. $0.33kW$
• C. $0.033kW$
• D. $33kW$

Answer 1

Answer: (A)

$3.3kW$

Answer 2

Work output of engine = mgh

= $100 \times 10 \times 10 = 10 ^ { 4 } \mathrm {~J}$

Efficiency (η) = $\frac { \text { output } } { \text { input } }$ ∴ Input energy =

$= \frac { 10 ^ { 4 } } { 60 } \times 100 = \frac { 10 ^ { 5 } } { 6 } \mathrm {~J}$

∴ Power = $\frac { \text { input energy } } { \text { time } }$

$\frac { 10 ^ { 5 } / 6 } { 5 } = \frac { 10 ^ { 5 } } { 30 } = 3.3 \mathrm {~kW}$