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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 m**

^{2}. (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 cm^{2}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 m**

^{3}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 10**

^{5}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}