​A boy of weight 600 N climbs up a rope through a height of takes 20 s to accomplish this task. What is the power expended by him?A boy of weight 600 N climbs up a rope through a height of 10 m.He takes 20 s to accomplish this task. What is the power expended by him?​

Correct option is A

The correct answer is (a) 300 W

Explanation:

The power expended by a person is given by the formula:

​$$P = \frac{W}{t}$$​​

Where:

• P is the power,
• W is the work done,
•  t is the time taken.

Step 1: Calculate the work done (W).

The work done is equal to the change in potential energy, which can be calculated as:

​$$W = \text{Weight} \times \text{Height}$$​​

Given:

• Weight = 600 N,
• Height = 10 m.
• time= 20 s

    $$W = 600 \, \text{N} \times 10 \, \text{m} = 6000 \, \text{J}$$​​

Step 2: Calculate the power.

Now, power is the work done divided by time:

       $$P = \frac{W}{t} = \frac{6000 \, \text{J}}{20 \, \text{s}} = 300 \, \text{W}$$​​

Thus, the power expended by the boy is 300 W.

Information Booster:

• Power Definition: Power is the rate at which work is done or energy is transferred. The standard unit of power is the watt (W), where $$1 \, \text{W} = 1 \, \text{J/s}$$​​
• Work Done in Lifting an Object: When lifting an object vertically against gravity, the work done is equal to the force (weight) multiplied by the distance moved (height).

Additional Knowledge:

• Work-Energy Theorem: The work done on an object is equal to the change in its energy. In this case, the work done is converting the boy’s energy to potential energy as he climbs.
• Unit Conversion: Power can also be measured in horsepower (hp), where $$1 \, \text{hp} = 746 \, \text{W}$$​, although watts are more commonly used for such calculations.