Answer: The weight of the rock in air is given by:
W = mg
where m is the mass of the rock and g is the acceleration due to gravity. Using the density of the rock, we can find its volume and hence its mass:
ρ = m/V --> m = ρV
where ρ is the density of the rock and V is its volume. The volume of the rock is:
V = m/ρ
Substituting the given values, we get:
V = (m/1900 kg/m^3)
The weight of the rock in air is equal to the tension in the string, which is 48.0 N. When the rock is submerged in water, it experiences an additional buoyant force due to the water. The buoyant force is given by:
F_b = ρ_w V g
where ρ_w is the density of water, V is the volume of the rock (which is the same as the volume of water displaced by the rock), and g is the acceleration due to gravity. Since the rock is completely submerged in water, its weight is balanced by the tension in the string and the buoyant force:
T - W - F_b = 0
Substituting the values for W, V, and F_b, we get:
T - mg - ρ_w V g = 0
T = mg + ρ_w V g
Substituting the given values, we get:
T = (1900 kg/m^3)(9.81 m/s^2)(0.05 m) + (1000 kg/m^3)(9.81 m/s^2)(0.05 m)
T = 220.5 N
Therefore, the tension in the string when the rock is submerged in water is 220.5 N.