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  4. A bucket full of water weighs 5 kg , it is pulled with constant speed from a well 20 m deep. There is a small hole in the bucket through which water leaks at a constant rate of 0.2 kg m- 1 . Ignore the force due to leakage. 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 with constant speed from a well $20 \, m$ deep. There is a small hole in the bucket through which water leaks at a constant rate of $0.2 \, kg \, m^{- 1}$ . Ignore the force due to leakage. The total work done in pulling the bucket up from the well is $\left(g = 10 \, m \, s^{- 2}\right)$

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
$\mathrm{W}=\int_{\mathrm{x}=20}^{\mathrm{x}=0}(5-0.2 \mathrm{x}) \times 10 \times \mathrm{dx} $ $=[50 \mathrm{x}]_{\mathrm{x}=0}^{\mathrm{x}=20}-\left[2 \frac{\mathrm{x}^2}{2}\right]_{\mathrm{x}=0}^{\mathrm{x}=20} $ $\mathrm{~W}=50 \times 20-(20)^2=600 \mathrm{~J}$