Question

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A : The power of a pump which raises 100 kg of water in 10 sec to a height of 100 m is 10 KW
Reason R : The practical unit of power is horse power
In light of the above statements, choose the correct answer from the options given below:

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

To test if Reason R is the correct explanation, read the two statements together using "because":
"The power is 10 kW *because* the practical unit of power is horsepower."
This clearly shows the two ideas are independent, making Option B the correct choice.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Power is defined as the rate of doing work.
In fluid mechanics, the hydraulic power (water horsepower) required to lift a specific mass of water is calculated from the potential energy delivered to that water mass per unit time.
Key Formula or Approach:
The formula for power ($P$) is: \[ P = \frac{W}{t} = \frac{m \times g \times h}{t} \] where: - $m$ is the mass of water lifted (in $\text{kg}$).
- $g$ is the acceleration due to gravity (approximately $9.81\text{ m/s}^2$, often rounded to $10\text{ m/s}^2$ for simplicity).
- $h$ is the height or lift head (in $\text{meters}$).
- $t$ is the time taken (in $\text{seconds}$).

Step 2: Detailed Explanation:
Let us analyze both statements:
1. Assertion A: The power of a pump which raises 100 kg of water in 10 sec to a height of 100 m is 10 KW.
Using the values provided:
- $m = 100\text{ kg}$
- $h = 100\text{ m}$
- $t = 10\text{ s}$
- $g \approx 10\text{ m/s}^2$
Substitute these values into the power equation: \[ P = \frac{100\text{ kg} \times 10\text{ m/s}^2 \times 100\text{ m}}{10\text{ s}} \] \[ P = \frac{100,000\text{ Joules}}{10\text{ s}} = 10,000\text{ Watts} = 10\text{ kW} \] If we use the more precise value $g = 9.81\text{ m/s}^2$, the power is $9.81\text{ kW}$, which rounds closely to $10\text{ kW}$.
Therefore, Assertion A is true.
2. Reason R: The practical unit of power is horse power.
In commercial and agricultural applications, pump power is standardly expressed in horsepower ($\text{HP}$), where $1\text{ HP} \approx 746\text{ Watts}$.
Therefore, Reason R is true.
However, the fact that horsepower is a practical unit of power does not explain how or why the pump's power is calculated to be $10\text{ kW}$ in Assertion A.
The calculation in Assertion A is based on physical laws of mechanics (work, force, and gravity), not on the choice of practical units.
Therefore, Reason R is not the correct explanation of Assertion A.

Step 3: Final Answer:
Both Assertion A and Reason R are true, but Reason R is not the correct explanation of Assertion A.
Hence, the correct option is (B).