# Upthrust, flotation and liquid pressure

1. Calculate the apparent weight in the following cases:
(a) 12 kg of iron immersed in water
(b) 3 kg of gold immersed in meths
(c) 5 kg of copper immersed in brine
(d) 8 kg of platinum immersed in mercury

2. Calculate the draught of a ferry of mass 20 000 metric tons sailing in seawater. Area of the base of the ferry = 2500 m2. (1 metric ton = 1000 kg).

3. A wooden rod, density 650 kgm-3 and one metre long floats upright in a liquid. If the cross sectional area of the rod is 4 cm2 calculate the depth to which it sinks in:
(a) water (b) meths (c) brine

4.A pure water ice cube with sides 2 cm long floats in a liquid in a glass beaker. What volume will be below the liquid surface if the liquid is:
(a) pure water (b) brine
What happens to the level of the water in the beaker if the ice cube melts and why?

5. A hot air balloon with a volume of 250 m3 hangs in the air. If the density of the hot air is 0.8 kgm-3 and that of the cool air outside the balloon is 1.2 kgm-3 what is the biggest load it can support if the fabric of the balloon and the basket have a total mass of 50 kg.

6. Calculate the total pressure:
(a) 2.5 m below the surface of water
(b) 0.5 m below the surface of mercury
(c) 3.5 m below the surface of brine
(Take the atmospheric pressure to be 105 Pa)

7. Calculate the difference if pressure between the top and bottom of a diving bell 2.5 m long immersed in water.

8. If the atmosphere was uniform and with the same density as that at sea level how high would it be. (Height of a mercury barometer = 0.76 m)

Data:
Density of brine                               = 1 150 kgm-3                   Density of meths             = 800 kgm-3
Density of water                              = 1000 kgm-3                    Density of sea water      = 1020 kgm-3
Density of mercury                         = 13600 kgm-3                   Density of ice                   = 950 kgm-3
Density of platinum                       = 21000 kgm-3               Density of gold                = 19000 kgm-3
Density of iron                  =                7800 kgm-3                     Density of copper         = 8930 kgm-3
Density of air at sea level            =      1.2 kgm-3