Answer:
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
