The terminal velocity of a copper ball of radius \(2.0\) mm falling through a tank of oil at \(20^{\circ}\text{C}\) is \(6.5~\text{cm/s}.\) What is the viscosity of the oil at \(20^{\circ}\text{C}\)? (Density of oil is \(1.5\times 10^{3}~\text{kg/m}^3,\) the density of copper is \(8.9\times10^{3}~\text{kgm}^{-3})\)
1. \(7.9\times 10^{-1}~\text{kgm}^{-1}\text{s}^{-1}\)
2. \(8.9\times 10^{-1}~\text{kgm}^{-1}\text{s}^{-1}\)
3. \(9.9\times 10^{-1}~\text{kgm}^{-1}\text{s}^{-1}\)
4. \(8.8\times 10^{-1}~\text{kgm}^{-1}\text{s}^{-1}\)

The lower end of a capillary tube of diameter \(2.00\) mm is dipped \(10.00\) cm below the surface of the water in a beaker. The pressure required in the tube in order to blow a hemispherical bubble at its end in water is? The surface tension of water at the temperature of the experiment is \(7.3\times 10^{-2}~\text{N/m},\) atmospheric pressure \(= 1.01\times 10^{5}~\text{Pa},\) the density of water \(= 1000~\text{kg m}^{-3}, g = 10~\text{ms}^{-2}.\)
1. \(1.01\times 10^{5}~\text{Pa}\)
2. \(2.02\times 10^{4}~\text{Pa}\)
3. \(1.03\times 10^{5}~\text{Pa}\)
4. \(2.01\times 10^{4}~\text{Pa}\)

The velocity of a small ball of mass \(M\) and density \(d\), when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(d\over 2\) then the viscous force acting on the ball will be:

A metal block of area \(0.10~\text{m}^{2}\) is connected to a \(0.010~\text{kg}\) mass via a string that passes over an ideal pulley (considered massless and frictionless), as in the figure below. A liquid film with a thickness of \(0.30~\text{mm}\) is placed between the block and the table. When released the block moves to the right with a constant speed of \(0.085~\text{m/s}.\) The coefficient of viscosity of the liquid is:

          
1. \(4.45 \times 10^{-2}~\text{Pa-s}\)
2. \(4.45 \times 10^{-3}~\text{Pa-s}\)
3. \(3.45 \times 10^{-2}~\text{Pa-s}\)
4. \(3.45 \times 10^{-3}~\text{Pa-s}\)

The flow of blood in a large artery of an anesthetised dog is diverted through a Venturi meter. The wider part of the meter has a cross-sectional area equal to that of the artery. A = 8 ${\mathrm{mm}}^2$. The narrower part has an area a = 4 ${\mathrm{mm}}^2$. The pressure drop in the artery is 24 Pa. What is the speed of the blood in the artery?

(Density of blood = $1.06\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

1.   145 m/s

2.   0.145 m/s

3.   123 m/s

4.   0.123 m/s