m mass of water in a tank has been frozen completely at 0 ∘ C . The height of frozen water is H . When the entire ice gets melted at 0 ∘ C , then the work done by gravity is (Specific gravity of ice a

Question

m mass of water in a tank has been frozen completely at 0 ∘ C . The height of frozen water is H . When the entire ice gets melted at 0 ∘ C , then the work done by gravity is (Specific gravity of ice at 0 ∘ C is 0.9)

TestHub · Accepted Answer

Melting lowers the height and centre of mass:
$H_{w a t er} = 0.9 H$
$h_{i} = H /2$
$h_{f} = 0.9 H /2$
Initial potential energy:
$U_{i} = m g \frac{H}{2} = 0.5 m g H$
Final potential energy:
$U_{f} = m g \frac{0.9 H}{2} = 0.45 m g H$
Work done by gravity:
$W = U_{i} - U_{f} = 0.5 m g H - 0.45 m g H$
$W = 0.05 m g H$

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