A rock with density 1900 kg/m3 is suspended from the lower end of a light string. When the rock is in air, the tension in the string is 48.0 NWhat is the tension in the string when the rock is totally immersed in a liquid with density 750 kg/m3?

the tension T2 when the rock is completely immersed is T2 = 29.05 N

Explanation:

from Newton's second law

F = m*a

where F = force, m = mass, a = acceleration

when the rock is suspended, a=0 since it is at rest. Then

T1 - m*g = 0, T1 = tension when suspended in air, g = gravity

assuming constant density of the rock

m = ρ rock * V, where ρ rock = density of the rock, V = volume

thus

T1 = m*g = ρ rock * g*V

V = T1 / (ρ rock * g)

when the rock is submerged in oil, it receives an upward force that equals the weight of the volume of displaced oil (V displaced). Since it is completely submerged the volume displaced is the volume of the rock V=Vdisplaced

When the rock is at rest, then

F = m*a=0

T2 + ρ oil * g*V displaced - ρ rock * g*V = 0

T2 = ρ rock * g*V - ρ oil * g*V = g*V (ρ rock - ρ oil)

T2 = g*V (ρ rock - ρ oil) = T1 / (ρ rock * g) * g * (ρ rock - ρ oil)

T2 = T1 * (ρ rock - ρ oil) / ρ rock

replacing values

T2 = 48 N * (1900 kg/m3 - 750 kg/m3) / 1900 kg/m3 = 29.05 N

T2 = 29.05 N