During Bentham’s lifetime, revolutions occurred in the American colonies and in France, producing the Bill of Rights and the Declaration des Droits deHomme (Declaration of the Rights of Man), both of which were based on liberty, equality, and self-determination. Karl Marx and Friedrich Engels published The Communist Manifesto in 1848. Revolutionary movements broke out that year in France, Italy, Austria, Poland, and elsewhere. In addition, the Indus trial Revolution transformed Great Britain and eventually the rest of Europe from an agrarian (farm-based) society into an industrial one, in which steam and coal increased manufacturing production dramatically, changing the nature of work, property ownership, and family. This period also included advances in chemistry, astronomy, navigation, human anatomy, and im munology, among other sciences.
Given this historical context, it is understandable that Bentham used reason and science to explain human behaviour. His ethical system was an attempt to quantify happiness and the good so they would meet the conditions of the scientific method. Ethics had to be empirical, quantifiable, verifiable, and reproducible across time and space. Just as science was beginning to understand the workings of cause and effect in the body, so ethics would explain the causal relationships of the mind. Bentham rejected religious authority and wrote a rebuttal to the Declaration of Independence in which he railed against natural rights as “rhetorical nonsense, nonsense upon stilts.” Instead, the fundamental unit of human action for him was utility—solid, certain, and factual.
What is utility? Bentham’s fundamental axiom, which underlies utilitarianism, was that all so cial morals and government legislation should aim for producing the greatest happiness for the greatest number of people. Utilitarianism, therefore, emphasizes the consequences or ultimate purpose of an act rather than the character of the actor, the actor’s motivation, or the particu lar circumstances surrounding the act. It has these characteristics: (1) universality, because it applies to all acts of human behaviour, even those that appear to be done from altruistic mo tives; (2) objectivity, meaning it operates beyond individual thought, desire, and perspective; (3) rationality, because it is not based in metaphysics or theology; and (4) quantifiability in its reliance on utility.
“We hold these truths to be self-evident: that all men are created equal and are endowed by their Creator with certain inalienable rights”.
This statement, in spite of literal inaccuracy in its every phrase, served the purpose for which it was written. It expressed an aspiration, and it was a fighting slogan. In order that slogans may serve their purpose, it is necessary that they shall arouse strong, emotional belief, but it is not at all necessary that they shall be literally accurate. A large part of each human being’s time on earth is spent in declaiming about his “rights,” asserting their existence, complaining of their violation, describing them as present or future, vested or contingent, absolute or conditional, perfect or inchoate, alienable or inalienable, legal or equitable, in rem or in personam, primary or secondary, moral or jural (legal), inherent or acquired, natural or artificial, human or divine. No doubt still other adjectives are available. Each one expresses some idea, but not always the same idea even when used twice by one and the same person.
They all need definition in the interest of understanding and peace. In his table of correlatives, Hohfeld set “right” over against “duty” as its necessary correlative. This had been done num berless times by other men. He also carefully distinguished it from the concepts expressed in his table by the terms “privilege,” “power,” and “immunity.” To the present writer, the value of his work seems beyond question and the practical convenience of his classification is convincing. However, the adoption of Hohfeld’s classification and the correlating of the terms “right” and “duty” do not complete the work of classification and definition.
Potato slices weighing 50 kg is dried from 60% moisture content (wet basis) to 5% moisture content (dry basis). The amount of dried potato slices obtained (in kg) is ............ (Answer in integer)
Two Carnot heat engines (E1 and E2) are operating in series as shown in the figure. Engine E1 receives heat from a reservoir at \(T_H = 1600 \, {K}\) and does work \(W_1\). Engine E2 receives heat from an intermediate reservoir at \(T\), does work \(W_2\), and rejects heat to a reservoir at \(T_L = 400 \, {K}\). Both the engines have identical thermal efficiencies. The temperature \(T\) (in K) of the intermediate reservoir is ........ (answer in integer). 
A bar of length \( L = 1 \, {m} \) is fixed at one end. Before heating its free end has a gap of \( \delta = 0.1 \, {mm} \) from a rigid wall as shown in the figure. Now the bar is heated resulting in a uniform temperature rise of \( 10^\circ {C} \). The coefficient of linear thermal expansion of the material is \( 20 \times 10^{-6} / \degree C \) and the Young’s modulus of elasticity is 100 GPa. Assume that the material properties do not change with temperature.
The magnitude of the resulting axial stress on the bar is .......... MPa (in integer). 
A massless cantilever beam, with a tip mass \( m \) of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length \( L = 1 \, {m} \), with a circular cross-section of diameter \( d = 20 \, {mm} \). The Young’s modulus of the beam material is 200 GPa.
The natural frequency of the spring-mass system is ............ Hz (rounded off to two decimal places).
A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm\(^2\), area moment of inertia of 7854 mm\(^4\), and a length \( L \) of 4 m. A point load \( P = 100 \, {N} \) acts at the center and an axial load \( Q = 20 \, {kN} \) acts through the centroidal axis as shown in the figure.
The magnitude of the offset between the neutral axis and the centroidal axis, at \( L/2 \) from the left, is ............ mm (rounded off to one decimal place).