When a body of mass $ m $ is raised to a height $ H $ against gravity, the potential energy of the body is:

Question

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The correct answer is Option A: increased by an amount $mgH$. When an object of mass $m$ is raised to a height $H$ against the constant force of gravity, work is done on the object. This work is stored as gravitational potential energy, resulting in an increase in the object's potential energy by an amount equal to $mgh$.

Step-by-Step Solution & Concepts:
When an object of mass $m$ is raised to a height $H$ against the constant force of gravity, work is done on the object. This work is stored as gravitational potential energy, resulting in an increase in the object's potential energy by an amount equal to $mgh$.

Working Principle: The gravitational potential energy ($PE$) of an object near the Earth's surface is defined by the work done to move it from a reference level to height $H$. Since the force required to lift the object at constant velocity is equal to its weight ($F = mg$), the work done is $W = F \cdot d = mgH$. Therefore, the change in potential energy $\Delta PE = mgh$.

Key Formulas: $W = \vec{F} \cdot \vec{d}$ — work done is the dot product of force and displacement; $PE = mgh$ — formula for gravitational potential energy near the surface of the Earth

Key Points: Potential energy is a form of energy related to the position of an object in a force field.; The reference point (where $h=0$) is arbitrary; only changes in height result in changes in energy.; Gravity is a conservative force, meaning work done depends only on the change in vertical height, not the path taken.

Advantages: Energy is conserved in a closed system under conservative forces.

Applications: Hydropower plants (using the height of water in a dam to generate electricity).; Physics of roller coasters and simple machines.

Additional Info: In the formula $PE = mgh$, $m$ is mass in kg, $g$ is acceleration due to gravity (approx $9.81 	ext{ m/s}^2$), and $h$ is height in meters.. Options B, C, and D are incorrect because they suggest a decrease in energy or a mathematically incorrect scaling factor.

Answer: A is correct — raising an object against gravity increases its gravitational potential energy by the product of its mass, the gravitational constant, and the vertical displacement.

Exam Tip: Remember that work done AGAINST a field results in a POSITIVE change in potential energy, whereas work done BY the field results in a NEGATIVE change in potential energy.

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Option B: decreased by an amount $mgH/2$

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Option C: increased by an amount $mgH/2$

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Option D: decreased by an amount $mgH$

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