The question asks about the most economical way to reduce project duration, which is known as "crashing" in project management. Crashing involves shortening the duration of activities by applying additional resources, which usually incurs extra cost. The goal is to reduce the project duration at the minimum possible additional cost.
A) Cheapest critical activity — Crashing a critical activity is essential to reduce the overall project duration. To do this economically, one must choose the critical activity that has the lowest cost per unit of time saved (i.e., the cheapest to crash).
The question asks to identify which substance among the given options does not react with concrete. Concrete is primarily composed of cement, aggregates, and water. Cement, when hydrated, forms calcium silicate hydrates and calcium hydroxide, which are alkaline in nature. Therefore, substances that are acidic or contain components that can react with these alkaline compounds will degrade concrete. We need to find the option that is chemically inert towards concrete.
Correct Option: D) Alcohol does not react with concrete. Alcohols are generally neutral and do not chemically attack the alkaline components of concrete like calcium hydroxide or calcium silicate hydrates. While they might penetrate the pores, they do not cause chemical degradation.
The problem asks for the porosity of a soil sample given its void ratio. We need to recall the fundamental relationship between porosity and void ratio in soil mechanics.
From the definitions, we can write:
\[ n = \frac{V_v}{V} = \frac{V_v}{V_v + V_s} \]To relate this to the void ratio, divide both the numerator and the denominator by \(V_s\):
\[ n = \frac{\frac{V_v}{V_s}}{\frac{V_v}{V_s} + \frac{V_s}{V_s}} \]\[ n = \frac{e}{e + 1} \]The problem states that the void ratio (\(e\)) is equal to unity, i.e., \(e = 1\).
Substitute \(e = 1\) into the derived formula:
\[ n = \frac{1}{1 + 1} = \frac{1}{2} \]To express porosity as a percentage, multiply by 100:
\[ n = \frac{1}{2} \times 100\% = 50\% \]Correct Option: B) 50.0% is the correct porosity when the void ratio is unity.
An optical square is a surveying instrument used for setting out right angles. It works on the principle of double reflection. The angle between the two mirrors in an optical square is fixed to ensure that the incident ray and the final reflected ray are at 90 degrees to each other.
Correct Option: C) 45
The question asks about the primary function of a theodolite in surveying. A theodolite is a precision optical instrument used for measuring angles in both the horizontal and vertical planes.
D) Measurement of both horizontal and vertical angles. This accurately describes the primary and most comprehensive function of a theodolite.
This question asks about the fundamental principle behind how aeroplanes generate lift and fly. We need to identify the physics principle that explains the pressure differences created by airflow over an aeroplane's wings.
Correct Option: C) Bernoulli's principle is the fundamental principle that explains how the shape of an aeroplane wing creates a pressure difference, resulting in lift.
The two-wattmeter method is a common technique for measuring three-phase power. The readings of the two wattmeters depend on the power factor of the load. When one wattmeter reads zero, it indicates a specific power factor angle.
In the two-wattmeter method for three-phase power measurement, the total power \(P_T\) is the sum of the readings of the two wattmeters, \(W_1\) and \(W_2\):
\[ P_T = W_1 + W_2 \]The individual wattmeter readings are given by:
\[ W_1 = V_L I_L \cos(30^\circ - \phi) \]\[ W_2 = V_L I_L \cos(30^\circ + \phi) \]where \(V_L\) is the line voltage, \(I_L\) is the line current, and \(\phi\) is the phase angle of the load (such that the power factor is \(\cos \phi\)).
We are given that the reading of one wattmeter is zero. Let's assume \(W_1 = 0\).
\[ 0 = V_L I_L \cos(30^\circ - \phi) \]Since \(V_L\) and \(I_L\) are non-zero for power measurement, it implies:
\[ \cos(30^\circ - \phi) = 0 \]For the cosine function to be zero, its argument must be \(90^\circ\) (or \(\pi/2\) radians).
\[ 30^\circ - \phi = 90^\circ \]Solving for \(\phi\):
\[ \phi = 30^\circ - 90^\circ = -60^\circ \]Alternatively, if we assume \(W_2 = 0\):
\[ \cos(30^\circ + \phi) = 0 \]\[ 30^\circ + \phi = 90^\circ \]\[ \phi = 90^\circ - 30^\circ = 60^\circ \]In both cases, the magnitude of the phase angle \(\phi\) is \(60^\circ\).
The power factor (\(PF\)) is given by \(\cos \phi\).
\[ PF = \cos(60^\circ) \]Calculating the value:
\[ PF = 0.5 \]B) 0.5 is the correct power factor when one wattmeter reads zero in the two-wattmeter method.
The question asks to identify which component is NOT a part of the electron gun in a Cathode Ray Oscilloscope (CRO). To answer this, we need to understand the basic structure and function of an electron gun and other parts of a CRO.
D) X - Y plates are the deflection plates, which are located after the electron gun assembly and are responsible for deflecting the electron beam horizontally and vertically to create the waveform on the screen. They are not part of the electron gun itself.
A strain gauge is a sensor whose resistance changes with applied strain. To measure this change in resistance, it is typically incorporated into a Wheatstone bridge circuit. The output of such a bridge, when unbalanced due to the resistance change, is a voltage.
Correct Option: A) The output quantity from a strain measuring device using a strain gauge, when connected in a bridge circuit, is a voltage. This voltage is proportional to the strain applied.
The question asks why the potentiometer method for DC voltage measurement is more accurate than using a voltmeter. The key to understanding this lies in how each device interacts with the circuit being measured.
Voltmeter measurement: A conventional voltmeter measures voltage by drawing a small current from the circuit. This current flow, however small, alters the original circuit conditions, leading to a slight drop in the voltage being measured. This effect is known as "loading the circuit." The internal resistance of the voltmeter is finite, and when connected in parallel, it reduces the equivalent resistance of that part of the circuit, thereby affecting the voltage.
Potentiometer measurement: A potentiometer, on the other hand, works on the principle of null deflection. It compares the unknown voltage with a known reference voltage. During the measurement process, when the potentiometer is balanced, no current flows from the unknown voltage source through the galvanometer. This means the potentiometer draws zero current from the circuit under test.
Impact on accuracy: Since the potentiometer draws no current from the circuit at the point of balance, it does not alter the original voltage or current distribution in the circuit. This ensures that the measurement obtained is the true, undisturbed voltage of the source. A voltmeter, by drawing current, always introduces some error due to its loading effect.
C) it does not load the circuit at all
This is the fundamental reason for the higher accuracy of a potentiometer. When balanced, a potentiometer draws no current from the source whose EMF or potential difference is being measured. Therefore, it does not disturb the circuit and measures the true value without any loading error.
A) it loads the circuit to maximum extent — This is incorrect. Loading the circuit to a maximum extent would mean drawing a large current, which would lead to significant errors and make the measurement highly inaccurate. This is the opposite of what a potentiometer does.
B) it loads the circuit moderately — This is also incorrect. While a voltmeter loads the circuit, a potentiometer's advantage lies in its ability to avoid loading the circuit entirely when balanced. Moderate loading would still introduce error.
D) it uses centre zero galvanometer instead of Voltmeters — While a potentiometer does use a centre zero galvanometer, this is a component used to detect the null point (zero current flow). The use of a galvanometer itself is not the direct reason for higher accuracy. The accuracy stems from the principle of null deflection, which implies no current draw, rather than just the type of indicator used.