IMAT 2011 Q74 [Density]

An object of mass 50 g just floats in a liquid of density 2.5 g/ml. When the object is placed in a liquid of density of 2.0 g/ml, it sinks to the bottom of the container. What is the force that the object exerts on the bottom of the container?

{ [g= 10m/s^2 = 10N/kg]}

A. 0.1N
B. 0.4N
C. 10N
D. 40N
E. 400N

For our first situation, with liquid 1, with the density of 2.5 g/ml we need to find the volume of said liquid in order to understand the value of it’s density.

For this we use the formula, Density= {\frac{mass}{volume}}
For it’s current purpose we can even re-write it as Volume= {\frac{mass}{volume}}
Volume= {\frac{mass}{volume}}= {\frac{50}{2.5}}= 20 mL

Using the same formula, we can now move onto the second liquid to calculate the mass of the water displaced.

Mass= {Density \times Volume}= { 2.0 g/ml\times 20 mL}= 40 g

Therefore, we can now say the buoyancy the object experiences from the water can be calculated using the formula they have provided or simply by using

W=mg where
W= Weight (N), m= Mass (kg), g= Gravitational Field ({10 N/kg})

W= mg= {\frac {40g}{1000}\times 10}= 0.4 N

Now we calculate the weight the object exerts onto the container using it’s provided mass of 50g, utilizing the same formula.

W= mg= {\frac {50g}{1000}\times 10}= 0.5 N

So we can see that the object exerts more force on the container, opposing the water’s buoyancy causing it to sink. To prove that, we subtract the values.

0.5N (Force exerted by object) - 0.4N (Water Buoyancy) = 0.1N (The force the object exerts at the bottom of the container)

Hence making the appropriate answer A.