Question

Give reason for your answer
(i) If an object has a density of 3.6 g/mL and you put it into the water, will it sink or float? (ii)Which box has a greater density?

Answer 1

It will sink

Box A has greater density

Answer 2

(i) The object will sink if put into the water. (ii) Box A has a greater density.

Given:

Density of the object (d) = 3.6 g/ml

To Find:

(i) Whether the object will sink or float.

(ii) Which box has a greater density.

Solution:

Part (i):

→ When an object is submerged in a liquid it experiences an upward buoyant force. For the same object, this buoyant force changes with the change in density of the liquid in which the object is submerged.

→ According to the Archimedes Principle when an object is immersed in a fluid, whether partially or fully, it experiences an upward buoyant force and this buoyant force is equal to the weight of the fluid displaced by the object.

• Weight of liquid displaced = Volume of Object (V) × Density of Liquid (ρ) × Acceleration due to gravity(g)

→ Hence the formula for Buoyant force (F) comes out to be: F=Vρg

→ If the density of the object is 'd' then the downward-acting weight of the body will be:

• Weight of body (W) = Volume of Object (V) × Density of object (d) × Acceleration due to gravity(g)  

→ Hence the formula for Weight (W) is given as W = Vdg  

→ The formula for the Net upward force is given as:                      

                        ∴ Net upward force = F - W = Vg × (ρ - d)

• If the density of the fluid is greater than or equal to the density of the object then the object will float.
• If the density of the fluid is smaller than the density of the object then the object will sink.

→ As we know the density of fluid that is water (ρ) = 1 g/ml

Since the density of water (ρ) is smaller than the density of the object (d), therefore the object will sink.

Part (ii):

→ The density of a material is equal to the mass that is present per unit volume. Hence we can define density as mass per unit volume.

                                $Density(\rho)=\frac{Mass(M)}{Volume(V)}$

→ If the volume remains constant then the density is directly proportional to the mass of the substance present.

→ In the given question, the volume of the box remains the same in both cases. Therefore the density will be directly proportional to the mass present in the two boxes.

As we can clearly see that the mass of the substance present in Box A is greater than the mass of the substance present in Box B.

Hence the density of Box A is greater than the density of Box B.

Therefore it can be said that (i) The object will sink if put into the water. (ii) Box A has a greater density.

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