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(A) : For drawing water with a bucket fr...

(A) : For drawing water with a bucket from a well by a person usage of pulley reduces the force required rather than drawing directly
(R) : When water is drawn with a bucket directly from well normal reaction on man is more man than that when he draws it using a pulley

A

Both (A) and (R) are true and (R) is the correct explanation of (A)

B

Both (A) and (R) are true and (R) is not the

C

(A) is true but ( R) is false

D

Both (A) and (R ) are false

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion (A) and the reason (R) provided. ### Step-by-Step Solution: 1. **Understanding the Assertion (A)**: - The assertion states that using a pulley reduces the force required to draw water with a bucket from a well compared to drawing it directly. - When a person draws water directly, they must exert a force equal to the weight of the bucket plus the water it contains. 2. **Analyzing the Direct Method**: - In the direct method, when a person pulls the bucket up, the force exerted (F) must overcome the gravitational force acting on the bucket (mg), where m is the mass of the bucket and water, and g is the acceleration due to gravity. - Thus, the force exerted by the person is F = mg. 3. **Understanding the Pulley System**: - When using a pulley, the tension (T) in the rope helps to lift the bucket. - The person exerts a force that creates tension in the rope, which acts upward on the bucket. - If the bucket is lifted with constant velocity, the tension in the rope equals the weight of the bucket: T = mg. 4. **Normal Reaction Force**: - The normal reaction force (N) acting on the person is affected by the force they exert while lifting the bucket. - In the direct method, the normal reaction force is greater because the person has to exert a force equal to the weight of the bucket (N = F + mg). - In the pulley method, the normal reaction force is less because the person only needs to exert a force equal to the tension in the rope (N = F - T). 5. **Comparing the Two Cases**: - In the direct method, the normal reaction force is higher because the person is directly lifting the weight of the bucket. - In the pulley method, the normal reaction force is lower because the tension in the rope helps to counteract the weight of the bucket. 6. **Conclusion**: - Both the assertion (A) and the reason (R) are true. - The assertion is supported by the explanation provided in the reason, which correctly describes why the normal reaction force is greater when drawing water directly compared to using a pulley. ### Final Answer: - **Assertion (A)**: True - **Reason (R)**: True - Both are correct, and the reason correctly explains the assertion.
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