Two cylindrical vessels of equal cross-sectional area of contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom, then the work done by the force of gravity is: (Density of water is and ) [2025]

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Solution

Q.
Two cylindrical vessels of equal cross-sectional area of $2 m^{2}$ contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom, then the work done by the force of gravity is: (Density of water is $10^{3} kg / m^{3}$ and $g = 10 m / s^{2}$ ) [2025]

1 $1 \times 10^{5} J$

2 $4 \times 10^{4} J$

3 $6 \times 10^{4} J$

4 $8 \times 10^{4} J$

Ans.
(4)

$U_{initial} = (ρ A \times 10) g \times 5 + (ρ A 6) g \times 3$

$U_{initial} = ρ A g (50 + 18) = 68 ρ A g$

$U_{final} = (ρ A \times 16) g \times 4 = (ρ A g) \times 64$

$W = △ U = 68 ρ A g - 64 ρ A g = 4 ρ A g$

$W = 4 \times 1000 \times 2 \times 10 = 8 \times 10^{4} J$

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