Published by:
CGP EDU Academic Team
Published on: September 13, 2026
A motor is capable of raising 400 kg of water in 5 minutes from a well 120 m deep. What is the power developed by the motor? [g = 10 m/sec 2 ]
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Calculate the work done in raising the water.
The work done (W) is given by the formula:
$$ W = mgh $$
where
- m = mass of the water = 400 kg
- g = acceleration due to gravity = 10 m/s2
- h = height = 120 m
Substituting the values:
$$ W = 400 imes 10 imes 120 $$
$$ W = 480000 ext{ J} $$
Step 2: Calculate the time taken in seconds.
The time taken = 5 minutes = 5 × 60 = 300 seconds.
Step 3: Calculate the power developed by the motor.
Power (P) is given by the formula:
$$ P = \frac{W}{t} $$
where
- W = work done = 480000 J
- t = time = 300 s
Substituting the values:
$$ P = \frac{480000}{300} $$
$$ P = 1600 ext{ W} $$
Step 4: Convert power to kilowatts (if necessary).
Since 1 W = 0.001 kW,
$$ P = 1600 ext{ W} = 1.6 ext{ kW} $$
Therefore, the power developed by the motor is 1600 W or 1.6 kW.
The work done (W) is given by the formula:
$$ W = mgh $$
where
- m = mass of the water = 400 kg
- g = acceleration due to gravity = 10 m/s2
- h = height = 120 m
Substituting the values:
$$ W = 400 imes 10 imes 120 $$
$$ W = 480000 ext{ J} $$
Step 2: Calculate the time taken in seconds.
The time taken = 5 minutes = 5 × 60 = 300 seconds.
Step 3: Calculate the power developed by the motor.
Power (P) is given by the formula:
$$ P = \frac{W}{t} $$
where
- W = work done = 480000 J
- t = time = 300 s
Substituting the values:
$$ P = \frac{480000}{300} $$
$$ P = 1600 ext{ W} $$
Step 4: Convert power to kilowatts (if necessary).
Since 1 W = 0.001 kW,
$$ P = 1600 ext{ W} = 1.6 ext{ kW} $$
Therefore, the power developed by the motor is 1600 W or 1.6 kW.
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