When a floating ice cube melts, the volume of watera)is less than the volume of the ice cubeb)is greater than the volume of the ice cubec)is equal to the volume of the ice cubed)none of the aboveCorrect answer is option 'C'. Can you explain this answer?

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EmSAT Achieve Exam > EmSAT Achieve Questions > When a floating ice cube melts, the volume of...

When a floating ice cube melts, the volume of water

a)
is less than the volume of the ice cube
b)
is greater than the volume of the ice cube
c)
is equal to the volume of the ice cube
d)
none of the above

Correct answer is option 'C'. Can you explain this answer?

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Verified Answer

When a floating ice cube melts, the volume of watera)is less than the ...

CONCEPT:

Archimedes' principle: A body at rest in a fluid is acted upon by a force pushing it upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.

The buoyant force (FB) is given by,

F_B = ρ_fluid × g × V_object

EXPLANATION:

The floating ice will displace some volume of the water.

From Archimedes' principle, F_B = ρ_water× g × V_ice ----(1)

Weight of the displaced fluid (water) = mg = ρ_water × V_{dispalced water} × g ----(2)

For an object to stay afloat, the forces acting on it must be balanced ⇒ (1) = (2)

ρ_water × g × V_ice = ρ_water × V_water× g

⇒ V_ice = V_{dispalced water}

Therefore, when the ice melts, there will be no change in the water level as the melted ice will occupy the same volume as that of displaced water.

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When a floating ice cube melts, the volume of watera)is less than the volume of the ice cubeb)is greater than the volume of the ice cubec)is equal to the volume of the ice cubed)none of the aboveCorrect answer is option 'C'. Can you explain this answer?

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