Correct Answer - Option 3 : Remain unchanged
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.
