An ice cube is floating in a tank filled with water. If the ice melts completely, then the water level in the tank will:

CONCEPT:

Density:

• It is defined as the mass per unit volume.
• The density is a scalar quantity.
• It is denoted by ρ.

⇒ \(ρ=\frac{m}{V}\)

Where m = mass and V = volume

Buoyant force:

• The buoyant force is the upward force exerted on an object wholly or partly immersed in a fluid. This upward force is also called Upthrust.
• Due to the buoyant force, a body submerged partially or fully in a fluid appears to lose its weight, i.e. appears to be lighter.
• The buoyant force is given as,

​⇒ F = ρVg

​Where ρ = density of fluid, V = volume displaced and g = gravitational acceleration

EXPLANATION:

Let F = buoyant force on ice cube, M = mass of the ice cube, ρ = density of water, V = volume of ice cube, and V' = volume of water displaced

• When ice cube is floating on the water the buoyant force will be equal to the weight of the ice.

⇒ F = ρV'g     -----(1)

Weight of ice cube,

⇒ w = Mg     -----(2)

By equation 1 and equation 2,

⇒ Mg = ρV'g

⇒ \(V'=\frac{M}{\rho}\)     -----(3)

• When the ice completes melts and is mixed with water, its density becomes equal to the water.
• When the ice melts completely the increase in the total volume of water is given as,

⇒ \( V_i=\frac{M}{\rho}\)     -----(4)

• By equations 3 and 4 we can say that the water level in the tank will not change. Hence, option 3 is correct.