Answer: According to the question, the distance traveled by the oscillator in one time period = 4A Where A represents the amplitude of the oscillation Therefore, the required ratio becomes = 4A/A =...
A hot air balloon is a sphere of radius 8 m. The sir inside is at a temperature of 60oC. How large a mass can the balloon lift when the outside temperature is 20oC?
Answer: Suppose that pi represents the pressure inside the balloon and po represents the pressure outside the balloon. Then the excess pressure can be written as: pi – po = 2T/r Where, T represents...
Surface tension is exhibited by liquids due to the force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Give that the latent heat of vaporisation for water Lv = 540 k cal/kg, the mechanical equivalent of heat J = 4.2 J/cal, density of water ρw = 103 kg/l, Avogadro’s number NA = 6.0 1026 k/mole, and the molecular weight of water MA = 18 kg for 1 k mole.
c) 1 g of water in the vapour state at 1 atm occupies 1601 cm3. Estimate the intermolecular distance at boiling point, in the vapour state. d) During vaporisation a molecule overcomes a force F,...
surface tension is exhibited by liquids due to the force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Give that the latent heat of vaporisation for water Lv = 540 k cal/kg, the mechanical equivalent of heat J = 4.2 J/cal, density of water ρw = 103 kg/l, Avogadro’s number NA = 6.0 1026 k/mole, and the molecular weight of water MA = 18 kg for 1 k mole.
a) Estimate the energy required for one molecule of water to evaporate. b) Show that the inter-molecular distance for water is Answer : a) According to the question, the latent heat of vaporization...
c) If po = 1.03 × 105 N/m2, ρo = 1.29 kg/m3 and g is 9.8 m/s2 at what height will the pressure drop to (1/10) the value at the surface of the earth? d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
Answer: (c) We know that - $ p={{p}_{0}}{{e}^{\left( -\frac{{{\rho }_{0}}gh}{{{p}_{0}}} \right)}} $ By substituting the known values, we can determine that h = 18.43 km (d) For $ \rho \alpha p $ to...
a) Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh? b) Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is ρo.
Answer: (a) The pressure falls as we ascend higher because the thickness of the gas above us diminishes. Let A be the cross-section of the air's horizontal layer, and dh be its height. The pressure...
The surface tension and vapour pressure of water at 20oC is 7.28 × 10-2 N/m and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20oC?
Answer: According to the question, the surface tension of water is T = 7.28 × 10-2 N/m and the vapour pressure is P = 2.33 × 103 Pa Let r represent the radius of the drop The excess pressure that is...
If a drop of liquid breaks into smaller droplets, it results in lowering of the temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature.
Answer: The volume of a drop of liquid with a radius of R = (N) (volume of a liquid droplet of radius r) $ \frac{4}{3}\pi {{R}^{3}}=N\times \frac{4}{3}\pi {{r}^{3}} $ $ N=\frac{{{R}^{3}}}{{{r}^{3}}}...
Two mercury droplets of radii 0.1 cm and 0.2 cm collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10-3 N/m.
Answer : The two drops should combine to make a larger drop in order to conserve volume. The radius of smaller drop is given as follows: r1 = 0.1 cm = 10-3 m Also, the radius of the bigger drop is...
The free surface of the oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a m/s2, what will be the slope of the free surface?
Answer: Let m be the mass of an elementary oil particle. The balancing forces are angled in the surface's direction. Pseudo force is given by ma mg represents the height of a small part of the oil...
The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius r = 2.5 × 10-5 m. The surface tension of sap is T = 7.28 × 10-2 N/m and the angle of contact is 0o. Does surface tension alone account for the supply of water to the top of all tress?
Answer: according to the question, the radius is r = 2.5 × 10-5 m The surface tension is T = 7.28 × 10-2 N/m It is also given that the angle of contact is θ = 0 degrees and the density is ρ = 103...
A cubical block of density ρ is floating on the surface of the water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upwards with acceleration a. What is the fraction immersed?
Answer : Let ρ represent the density of a block and let height of the block be L Then, we can write the expression for the mass of the block as follows: m = Vρ = L3ρ Then, the weight of the block is...
A cubical block of density ρ is floating on the surface of the water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upwards with acceleration a. What is the fraction immersed?
Answer : Let ρ represent the density of a block and let height of the block be L Then, we can write the expression for the mass of the block as follows: m = Vρ = L3ρ Then, the weight of the block is...
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass M and density ρ is suspended by a massless spring of spring constant k. This block is submerged inside into the water in the vessel. What is the reading of the scale?
Answer: We know that the upthrust of the block is equal to the weight of water displaced. The expression of which can be written as follows Vρwg Let x represent the compression in the spring. So,...
An iceberg floats in water with part of it submerged. What is the fraction of the volume of an iceberg submerged if the density of ice is ρi = 0.917 g/cm3?
Answer: According to the question, the density of ice is ρice = 0.917 g/cm3 The density of water is ρwater = 1 g/cm3 Let Vi represent the volume of the iceberg and Vw denote the volume of the water...
Is surface tension a vector?
Answer: Surface tension is a scalar quantity as it has a specific direction. Surface tension is given by the expression : σ = W.D / Change in surface area As it is equal to the work done per unit...
Is viscosity a vector?
Answer: Viscosity is not a vector quantity. Viscosity is a liquid attribute that's equal to the amount of dragging force per unit area between two liquid layers with the same velocity gradient. As a...
Streamline flow is more likely for liquids with
a) high density b) high viscosity c) low density d) low viscosity Answer: The correct options are : b) high viscosity c) low density Explanation: Streamline flow is highly likely for liquids with...
With increase in temperature, the viscosity of
a) gases decreases b) liquids increases c) gases increases d) liquids decreases Answer: The correct options are : c) gases increases d) liquids decreases Explanation : Because the viscosity of...
A wooden block with a coin placed on its top, floats in water as shown in the figure:
The distance l and h are shown in the figure. After some time the coin falls into the water. Then a) l decreases b) h decreases c) l increases d) h increases Answer: The correct options are : a) l...
Pressure is a scalar quantity because
a) it is the ratio of force to the area and both force and area are vectors b) it is the ratio of the magnitude of the force to area c) it is the ratio of a component of the force normal to the area...
For a surface molecule
a) the net force on it is zero b) there is a net downward force c) the potential energy is less than that of a molecule inside d) the potential energy is more than that of a molecule inside Answer:...
The angle of contact at the interface of water-glass is 0o, ethyl alcohol-glass is 0o, mercury-glass is 140o, and methyl iodide-glass is 30o. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is
a) water b) ethyl alcohol c) mercury d) methyl iodide Answer : The correct answer c) mercury If the contact angle is obtuse, the liquid meniscus in a capillary tube will be convex upwards. When one...
An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is
a) 9:4 b) 3:2 c) √3: √2 d) √2: √3 Answer: The correct answer a) 9:4 $ {{A}_{1}}{{v}_{1}}={{A}_{2}}{{v}_{2}} $ $ \frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{A}_{1}}}{{{A}_{2}}}={{\left(...
Along a streamline
a) the velocity of a fluid particle remains constant b) the velocity of all fluid particles crossing a given position is constant c) the velocity of all fluid particles at a given instant is...
Which of the following diagrams does not represent a streamline flow?
The correct answer is d) Lines of flow do not intersect each other.
A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).
Answer: The correct answer is c)
In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.
Answer : Answer : (a) If dissipative forces exist, some forces in the liquid flow due to pressure difference are expended against dissipative forces, resulting in a high-pressure drop. (b) Due to...
A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm2. What maximum pressure would the smaller piston have to bear ?
Answer : Given: according to the question, the maximum mass that can be lifted is given as m = 3000 kg and the area of a cross-section of the load-carrying piston is A = 425 cm2 = 425 × 10-4 m2...