Answer:
To solve this problem, we need to use the concept of buoyancy. When an object is submerged in a fluid, it experiences a buoyant force, which is equal to the weight of the fluid displaced by the object. This buoyant force reduces the apparent weight of the object.
Let's start by finding the weight of the rock in air:
Weight of rock in air = mass of rock x acceleration due to gravity
= 0.6 kg x 9.8 m/s^2
= 5.88 N
Now, let's find the weight of the fluid displaced by the rock when it is submerged in water:
Weight of fluid displaced = mass of fluid displaced x acceleration due to gravity
The mass of fluid displaced is equal to the volume of the rock submerged in water times the density of water. We can use the apparent mass of the rock to find the volume submerged in water:
Volume submerged in water = (weight of rock in air - weight of rock in water) / (density of water x acceleration due to gravity)
= (5.88 N - 3.75 N) / (1000 kg/m^3 x 9.8 m/s^2)
= 0.0228 m^3
Now, we can find the weight of fluid displaced by the rock:
Weight of fluid displaced = 0.0228 m^3 x 1000 kg/m^3 x 9.8 m/s^2
= 224.16 N
The buoyant force acting on the rock is equal to the weight of fluid displaced:
Buoyant force = 224.16 N
Therefore, the weight of the rock when submerged in water is:
Weight of rock in water = Weight of rock in air - Buoyant force
= 5.88 N - 224.16 N
= -218.28 N
The negative sign indicates that the buoyant force is acting in the upward direction, opposing the weight of the rock.
Now, we can find the density of the rock using the formula:
Density = mass / volume
The mass of the rock is 0.6 kg, and the volume of the rock is equal to the volume submerged in water:
Density = 0.6 kg / 0.0228 m^3
= 26.32 kg/m^3
Therefore, the density of the rock is 26.32 kg/m^3.
Step-by-step explanation:
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