An object of mass 50 g floats in a liquid of density 2.5 g/ml. When the object is placed in a liquid of density 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]
To find the force that the object exerts on the bottom of the container, we need to understand the concept of buoyancy.
The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This force counteracts the weight of the object, causing it to either float or sink.
First, let's calculate the weight of the object in air:
Weight = mass * acceleration due to gravity
Weight = 50 g * 10 m/s^2
Weight = 500 g (or 0.5 kg) * 10 m/s^2
Weight = 5 N
Next, let's calculate the volume of the object. We can use the density of the liquid and the mass of the object:
Volume = mass / density
Volume = 50 g / 2.5 g/ml
Volume = 20 ml (or 0.02 L)
Now, let's find the buoyant force when the object is in the liquid with a density of 2.5 g/ml:
Buoyant force = weight of liquid displaced by the object
Buoyant force = density of liquid * volume of object * acceleration due to gravity
Buoyant force = 2.5 g/ml * 0.02 L * 10 m/s^2
Buoyant force = 0.5 N
Finally, when the object is placed in the liquid with a density of 2.0 g/ml, it sinks to the bottom of the container. In this case, the buoyant force is not enough to counteract the weight of the object, so the net force acting on the object is its weight (5 N).
Therefore, the force that the object exerts on the bottom of the container is 5 N.