In a car lift, the compressed air exerts a force \(F_1\) on a small piston having a radius of \(5.0\) cm. This pressure is transmitted to the second piston of a radius of \(15\) cm. If the mass of the car to be lifted is \(1350\) kg, the pressure necessary to accomplish this task and the force \(F_1,\) respectively, are? (\(g = 9.8\) ms^–2)
1. \(1.9\times 10^{6}~\text{Pa}~\text{and}~1400~\text{N}\)
2. \(1.9\times 10^{4}~\text{Pa}~\text{and}~1580~\text{N}\)
3. \(19\times 10^{5}~\text{Pa}~\text{and}~1570~\text{N}\)
4. \(1.9\times 10^{5}~\text{Pa}~\text{and}~1470~\text{N}\)

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

A metal block of area \(0.10~\text{m}^{2}\) is connected to a \(0.010\) 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 \(0.30\) mm is placed between the block and the table. When released the block moves to the right with a constant speed of \(0.085\) 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 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. \(2.01\times 10^{4}~\text{Pa}\)

Two syringes of different cross-sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are \(1.0\) cm and \(3.0\) cm respectively. Force exerted on the larger piston when a force of \(10\) N is applied to the smaller piston:
1. \(80\) N
2. \(90\) N
3. \(10\) N
4. \(20\) N