Fluid Statics

Practice Questions:

Question 1: difficult

A cylindrical piece of cork of density \[\rho\] of base area A and height h floats in a liquid of density \[\rho\acute{}\]. The cork is slightly depressed and then released. The time period of oscillation of the cork is :

1. \[\pi\sqrt{\frac{g\rho\acute{}}{g\rho}}\]

2. \[\pi\sqrt{\frac{h\rho}{g\rho\acute{}}}\]

3. \[2\pi\sqrt{\frac{h\rho\acute{}}{g\rho}}\]

4. \[2\pi\sqrt{\frac{h\rho}{g\rho\acute{}}}\]

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Question 2: difficult

Two non-mixing liquids of densities \[\rho\] and \[n\rho(n>1)\] are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p < 1) in the denser liquid. The density d is equal to :

1. \[\left\{ {1+(n+1)p} \right\}\rho\]

2. \[\left\{ {2+(n+1)p} \right\}\rho\]

3. \[\left\{ {2+(n-1)p} \right\}\rho\]

4. \[\left\{ {1+(n-1)p} \right\}\rho\]

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Question 3: difficult

A tank contains water on top of mercury as shown in figure. A cubical block of side 10 cm is in equilibrium inside the tank. The depth of the block inside mercury is (RD of the material of block = 8.56, RD of mercury = 13.6)

1. 6 cm

2. 5 cm

3. 7 cm

4. 8 cm

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