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  4. A bucket full of water weighs 5 kg , it is pulled from a well 20 m deep. There is a small hole in the bucket through which water leaks at a constant rate. If it is observed that for every metre the bucket loses 0.2 kg mass of water, then the total work done in pulling the bucket up from the well is [ g=10 m s- 2 ]

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Q. A bucket full of water weighs $5 \, kg$ , it is pulled from a well $20 \, m$ deep. There is a small hole in the bucket through which water leaks at a constant rate. If it is observed that for every metre the bucket loses $0.2 \, kg$ mass of water, then the total work done in pulling the bucket up from the well is [ $g=10 \, m \, s^{- 2}$ ]

NTA AbhyasNTA Abhyas 2020Work, Energy and Power

Solution:

The weight of bucket when it has been pulled up a distance $x \, is \, (5-0.2\,x)$
Hence, the required work is
$W=\displaystyle \int _{x = 20}^{x = 0} - \left(5 - 0.2 x\right) \times 10 \times d x$
$=\left[50 x\right]_{x = 0}^{x = 20}-\left[2 \frac{x^{2}}{2}\right]_{x = 0}^{x = 20}$
$W=50\times 20-\left(20\right)^{2}=600 \, J$