The mass of bucket full of water is 15 kg. It is being pulled up from a 15m deep well. Due to a hole in the bucket 6 kg water flows out of the bucket . The work done in drawing the bucket out of the well willbe (g = 10m/ $s^{2}$ )-

900 J

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1500 J

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1800 J

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2100 J

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Solution

The correct option is C 1800 J
Given,
$m = 15 k g$
$g = 10 m / s^{2}$
$x = 15 m$
Mass varies from the deep of well to height $x = 15 m$
Let consider, $ϕ$ is change in mass per unit length
$ϕ = \frac{d m}{d x}$
$d m = ϕ d x = \frac{6}{15} d x$
Mass of water left in bucket, $M = m - d m$
Work done, $W = F . x$ , change in potential energy
$W = (M g) . x$
$W = (m - d m) g x$
$W = m g x - d m g x d x$
$W = m g x - d m g \frac{x^{2}}{2}$
$W = 15 \times 10 \times 15 - \frac{6}{15} \times 10 \frac{15 \times 15}{2}$
$Q = 2250 - 450$
$W = 1800 J$
The correct option is C.

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The mass of bucket full of water is 15 kg. It is being pulled up from a 15m deep well. Due to a hole in the bucket 6 kg water flows out of the bucket . The work done in drawing the bucket out of the well willbe (g = 10m/s2)-

The mass of bucket full of water is 15 kg. It is being pulled up from a 15m deep well. Due to a hole in the bucket 6 kg water flows out of the bucket . The work done in drawing the bucket out of the well willbe (g = 10m/ $s^{2}$ )-