If a man lifts $ 1 ext{ kg}$ of load to the height of $ 2.5 ext{ m}$ from the ground, then assuming accelera

Question

If a man lifts $ 1	ext{ kg}$ of load to the height of $ 2.5	ext{ m}$ from the ground, then assuming acceleration due to gravity is $ 10	ext{ m/sec}^2 $, magnitude of the work done by the man is ________.

Examoogle · Accepted Answer

The correct answer is Option B: 25 joules. When a man lifts a $1	ext{ kg}$ load to a height of $2.5	ext{ m}$, the work done against gravity is equal to the gravitational potential energy gained by the load. Using the formula $W = m 	imes g 	imes h$, substituting $m = 1	ext{ kg}$, $g = 10	ext{ m/sec}^2$, and $h = 2.5	ext{ m}$ gives $W = 1 	imes 10 	imes 2.5 = 25	ext{ joules}$.

Step-by-Step Solution & Concepts:
When a man lifts a $1	ext{ kg}$ load to a height of $2.5	ext{ m}$, the work done against gravity is equal to the gravitational potential energy gained by the load. Using the formula $W = m 	imes g 	imes h$, substituting $m = 1	ext{ kg}$, $g = 10	ext{ m/sec}^2$, and $h = 2.5	ext{ m}$ gives $W = 1 	imes 10 	imes 2.5 = 25	ext{ joules}$.

Working Principle: Work done is defined as the scalar product of force and displacement. When an object is lifted vertically at a constant speed, the upward force exerted by the man is equal in magnitude to the downward gravitational force (weight $W = mg$). The work done by the lifting force is positive because the force and displacement are in the same upward direction.

Key Formulas: $W = F \cdot s = mgh$ — Work done against gravity; $W = m 	imes g 	imes h$ — Gravitational potential energy formula

Key Points: Work done by an external lifting force against gravity is positive because force and displacement are in the same direction.; The SI unit of work and energy is the joule ($J$), which is equivalent to $	ext{N}\cdot	ext{m}$ or $	ext{kg}\cdot	ext{m}^2	ext{/s}^2$.; Mass $m = 1	ext{ kg}$, Acceleration due to gravity $g = 10	ext{ m/sec}^2$, Height $h = 2.5	ext{ m}$.

Advantages: Simple direct application of the work-energy theorem and gravitational potential energy.

Applications: Calculating energy expended by humans or cranes in lifting objects against gravity.; Determining potential energy storage in hydroelectric dams.

Additional Info: Option B is 25 joules, which matches the calculated product $1 	imes 10 	imes 2.5$.. Options A, C, and D represent arithmetic errors in decimal placement or multiplication.

Answer: B is correct — 25 joules is the magnitude of the work done by the man in lifting the load.

Exam Tip: Always verify units before multiplying values in physics numerical problems to avoid common decimal shifting errors.

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