Question

45. A motor of 100W takes 20 second to lift 10 kg water to a height of
10m. The efficiency of motor is
a) 100%
b) 50% c) 25% d) 150%​

Answer 1

Answer:

$\boxed{\mathfrak{(b) \ 50\%}}$

Given:

Input Power ($\sf P_i$)= 100 W

Mass (m) = 10 kg

Height (h) = 10 m

Time (t) = 20 s

To Find:

Efficiency of the motor

Explanation:

$\star$ Output power of the motor:

$\boxed{ \bold{Out put \: power \: (P_o)= \frac{mgh}{t}}}$

$\sf \implies P_o = \frac{10 \times 10 \times 10}{20} \\ \\ \sf \implies P_o = \frac{1000}{20} \\ \\ \sf \implies P_o = \frac{ \cancel{20} \times 50}{ \cancel{20}} \\ \\ \sf \implies P_o = 50 \: W$

$\star$ Efficiency of the motor:

$\boxed{ \bold{Efficiency = \frac{Out put \ Power \ (P_o)}{In put \ Power \ (P_i)} \times 100}}$

$\sf \implies Efficiency = \frac{50}{ \cancel{100}} \times \cancel{100} \\ \\ \sf \implies Efficiency = 50 \: \%$

$\therefore$

Efficiency of the motor = 50 %

Answer 2

Answer:

Efficiency = Output power/Input power × 100

Input Power = 100W

Output Power = mgh/t

= 50 W

So,

Efficiency = 50/100 × 100

= 50%