MPSC 2021 Prelims Paper-I · Question 55 of 100

Correct — option (2), 40.83 W. The chain here is short and every link is a definition. Work done against gravity in raising a mass is the force times the distance moved in the direction of the force; the force needed is the weight, which is mass times the acceleration due to gravity, so the work is W = mgh. Power is the rate of doing work, that is P = W / t, and its SI unit is the watt, which is one joule per second. Substituting the values in the stem with g taken as 9.8 m s⁻², the work is 25 × 9.8 × 5 = 1225 joules, and the power is 1225 ÷ 30 = 40.83 watts. That is the whole calculation, and each of the two steps corresponds to one of the wrong options, which is how the option set was built. It is worth noticing two things about the arithmetic. First, the answer is insensitive to the value used for g: taking g as 10 m s⁻² instead gives 25 × 10 × 5 = 1250 joules and 1250 ÷ 30 = 41.67 watts, which is nearest to the same option, so a candidate who habitually rounds g need not worry here. Second, the magnitude is physically sensible. Forty watts is a modest and entirely human rate of working — about the power of an old incandescent bulb, and roughly a twentieth of a horsepower, which is 746 watts — and that is what one expects from a person taking a full half-minute to climb five metres with a load. A candidate who arrives at a figure in the hundreds or thousands of watts has produced a person doing the work of a small motor, and the sanity check alone eliminates two of the three wrong rows. The printed English of this item is awkward — it prints 'upto' as one word and the ungrammatical 'How much power the man needs to carry the bag ?' — but the physics asked for is unambiguous, and the card reproduces the stem as printed.

• (1)1225 W — This is the WORK done, not the power, and it is the answer of a candidate who stops one step early. Raising 25 kilograms through 5 metres against gravity takes 25 × 9.8 × 5 = 1225 joules, and that number is correct as far as it goes; what has gone wrong is the label attached to it. Power is work divided by the time taken, and the thirty seconds printed in the stem has simply not been used. The unit is the giveaway, and it is worth training the eye to catch it: the joule measures energy and the watt measures energy per second, so the same figure cannot serve for both. A useful discipline in any numerical item is to ask, before choosing, which of the given quantities has not yet appeared in the working — if a number printed in the stem has played no part in the answer, the answer is almost certainly incomplete. Here the unused number is the time, and the time is precisely what turns work into power.
• (3)1.64 W — This is the same calculation with the mass left out — 1 × 9.8 × 5 ÷ 30 gives about 1.63 — so it is the power required to raise one kilogram rather than the twenty-five kilograms the stem specifies. Equivalently it is the correct answer divided by 25. The error usually happens when a candidate sets out the formula P = mgh / t correctly, substitutes g, h and t, and then loses m either by treating the mass as already contained in the weight or by cancelling it in a hurried rearrangement. There is also a conceptual version of the same slip, in which the figure is read as a power 'per kilogram' and accepted as though the question had asked for a specific quantity. It did not: it asked how much power the man needs, which is a total, and a total must carry the total mass. A quick check of magnitude helps here too, since 1.6 watts is less than the power of a small torch bulb and cannot describe a person climbing stairs with a load.
• (4)245 W — This is the WEIGHT of the load expressed as a number — 25 kg × 9.8 m s⁻² = 245 newtons — with the wrong unit written after it. It is the first intermediate quantity in the calculation, obtained before either the height or the time has been used, so the answer discards two of the four numbers the stem supplies. The mislabelling is what makes it plausible: 245 is a number that genuinely comes out of the problem, and a candidate who has computed it correctly may accept the row on the strength of recognising the figure. Recognising a figure is not the same as checking what it measures. The newton measures force, the joule measures work, and the watt measures work per unit time; carrying the units through every line of the working, rather than attaching them at the end, is what keeps the three apart. Of the four rows in this set, three are numerically genuine quantities from within the calculation and only one of them is the quantity asked for.

Work, energy and power form one small family of definitions that MPSC returns to constantly, and holding them apart by their units is the most reliable way to keep them straight. Work is done when a force moves its point of application, and it equals the force multiplied by the displacement in the direction of the force; its unit is the joule, which is one newton-metre. No work is done, in the physicist's sense, by a force perpendicular to the motion, nor by a man standing still holding a heavy suitcase however tired he becomes, because nothing moves through the force. Energy is the capacity to do work and is measured in the same unit; the two forms met earliest are kinetic energy, ½mv², and gravitational potential energy near the earth's surface, mgh. Raising a mass converts work into potential energy, which is why the work done in this problem equals the gain in potential energy of the load. Power is the rate at which work is done or energy is transferred, measured in watts, one watt being one joule per second, with the kilowatt and the horsepower — about 746 watts — as the practical larger units. The kilowatt-hour, which appears on an electricity bill, is not a unit of power at all but of energy: one kilowatt sustained for one hour, or 3.6 million joules. That distinction between a rate and a total is the single most examined point in this part of the syllabus, and it is exactly what separates the correct row from the first wrong one in this question.

Each MPSC prelims paper carries a handful of one-step numerical items in its science section, and they are set so that the arithmetic can be done mentally or with a line of working. What is being tested is not calculation but whether a candidate can identify which quantity the question asks for and which formula produces it. The option set in a well-made item of this type is therefore built from the intermediate results of the correct calculation, and this one is a textbook example: 245 is the weight, 1225 is the work, 1.64 is the work per kilogram per second, and only 40.83 is the power. Three of the four rows are real numbers from the problem wearing the wrong unit. The lesson is to carry units through every line rather than to compute bare numbers and label them at the end, and to check before choosing that every quantity printed in the stem has been used. Note the printed English as well. The stem writes 'upto' as a single word and ends with the ungrammatical 'How much power the man needs to carry the bag ?', and the Marathi column carries the corresponding sentence; both are reproduced here as printed rather than repaired, since the stem belongs to the Commission and not to this card.

• Work done against gravity in raising a mass is W = mgh, measured in joules; power is the rate of doing work, P = W / t, measured in watts, where one watt is one joule per second.
• For this problem: W = 25 × 9.8 × 5 = 1225 joules, and P = 1225 ÷ 30 = 40.83 watts.
• Taking g as 10 m s⁻² instead of 9.8 gives 1250 joules and 41.67 watts, which points to the same option, so the answer does not depend on how g is rounded.
• The three wrong options are all genuine quantities from within the calculation carrying the wrong unit: 245 is the weight in newtons, 1225 is the work in joules, and 1.64 is the figure obtained if the mass is omitted.
• One horsepower is about 746 watts, so a rate of about 41 watts is roughly a twentieth of a horsepower — a plausible human output for climbing five metres in half a minute.
• The kilowatt-hour is a unit of ENERGY, not of power: one kilowatt sustained for one hour, equal to 3.6 × 10⁶ joules, which is the distinction this question's first wrong option turns on.

• Reporting the work done when the power was asked for, which is the same figure with the time step omitted
• Leaving out a quantity the stem supplied — if a printed number has played no part in the working, the answer is almost certainly incomplete
• Attaching the wrong unit to a genuine intermediate result, since the newton, the joule and the watt measure force, energy and rate of energy transfer respectively
• Losing the mass in the rearrangement and computing a per-kilogram figure where a total was asked for
• Failing to check the magnitude against everyday experience, when a human being cannot plausibly work at hundreds or thousands of watts

Mechanics numericals in MPSC papers stay at one or two steps and draw on a very small set of formulae — F = ma, W = Fd, P = W/t, the equations of uniformly accelerated motion, and the expressions for kinetic and potential energy. The examiner's usual device is the option set: the correct value is printed alongside the intermediate results of the same calculation, so that stopping early or starting late lands on a row that exists. A second device is the unit, with a numerically correct figure offered under the wrong name, as happens twice in this question. A third is the conceptual variant, which asks not for a number but for whether work is done at all in a described situation. Preparing for all three means practising with units written on every line, and finishing every numerical by asking two questions: have I used every number the stem gave me, and is the size of my answer physically believable ?

No directly related past PYQ was found.

• practice — not a real PYQ

  A machine lifts a load of 50 kg through a height of 4 metres in 10 seconds. Taking g as 10 m s⁻², what is the power developed ?

  • (a)200 W
  • (b)500 W
  • (c)2000 W
  • (d)20 W

  Answer(a) 200 W — the work done against gravity is mgh = 50 × 10 × 4 = 2000 joules, and the power is that work divided by the time taken, 2000 ÷ 10 = 200 watts. The figure of 2000 in the third option is the work done in joules rather than the power, which is the commonest error in this calculation; 500 is the weight of the load in newtons, again a genuine intermediate quantity wearing the wrong unit.

• practice — not a real PYQ

  In which of the following situations is no work done, in the physicist's sense of the term ?

  • (a)A porter climbing a staircase with a suitcase on his head
  • (b)A man standing still and holding a heavy suitcase in his hand
  • (c)A horse pulling a cart along a level road
  • (d)A stone falling freely under gravity

  Answer(b) A man standing still and holding a heavy suitcase in his hand — work requires a force to move its point of application, and here nothing moves, so no work is done however tiring the effort feels. The porter climbing the stairs raises the suitcase against gravity and does work equal to mgh; the horse applies a force through a displacement along the road; and gravity does work on the falling stone, converting its potential energy into kinetic energy.