Question

A person pulls a bucket of water from a well of depth h. if the mass of uniform rope is m and that of the bucket full of water is m, then work done by the person is_____

a. (M + m/2) gh
B. ½ (M + m) gh
C. (M + m) gh
D. (M/2 + m) gh

Answer 1

The work done by a person lifting a bucket from a well is calculated by adding the work done on the bucket (mgh) and the work done on the uniform rope ((M/2)gh), resulting in the correct answer of D. (M/2 + m)gh.

Step-by-step explanation:

To determine the work done by a person pulling a bucket of water from a well, we need to consider both the mass of the bucket full of water (m) and the mass of the uniform rope (M). As the bucket is pulled up at constant speed, the force required to lift it is mg, and the work done on the bucket is mgh. The rope, however, is distributed evenly, and only half of its mass (M/2) would be considered at the average height (h/2). Hence, the work done lifting the rope is (M/2)(g)(h). Summing the work done on both the bucket and the rope gives the total work W = mgh + (M/2)gh, which simplifies to W = (M/2 + m)gh. Therefore, the correct answer is D. (M/2 + m)gh.