A body of mass $m$ is taken from the ground to a height $h$, t... | General Science MCQ

General SciencePrevious Year Paper 2024

A body of mass $m$ is taken from the ground to a height $h$ , the gravitational potential energy of the body will be: Acceleration due to gravity is $g$ .

$mgh$

$\frac{1}{2}mv^2$

$F \times d$

$mg$

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option A

$mgh$

Quick Summary:

The gravitational potential energy ( $PE$ ) of a body of mass $m$ at a height $h$ above the ground in a uniform gravitational field is given by the product of its mass, the acceleration due to gravity ( $g$ ), and the height ( $h$ ), which is expressed as $mgh$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Lifting a heavy stone from the ground to a tabletop requires you to do work against gravity. The higher you lift it, or the heavier the stone is, the more energy it stores—which is why it can do more damage or release more energy if it falls back down.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'mgh' as 'Mass Gives Height' energy.

🔢 Key Formulas

$PE = mgh$ — Gravitational Potential Energy near Earth's surface

$W = \Delta PE = mgh$ — Work-Energy Theorem for lifting a body

⚙️ Working Principle

When a body of mass $m$ is lifted vertically upwards through a height $h$ at a constant speed, work is done against the downward gravitational force ( $F = mg$ ). The work done in lifting the body is stored inside the body as potential energy. Since work $W = \text{Force} \times \text{Displacement} = (mg) \times (h)$ , the gravitational potential energy gained by the body is $PE = mgh$ .

📌 Key Points

▸
Gravitational potential energy depends linearly on the mass ( $m$ ) of the body, acceleration due to gravity ( $g$ ), and height ( $h$ ).
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It is measured in Joules ( $\text{J}$ ) or $\text{kg} \cdot \text{m}^2\text{s}^{-2}$ .
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The reference level where potential energy is assumed to be zero is chosen arbitrarily, usually taken at the ground level.

✅ Advantages

▸
Simple and accurate formula for uniform gravitational fields near the Earth's surface.

❌ Disadvantages / Limitations

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Not valid for large heights where $g$ varies significantly with altitude ( $h$ comparable to Earth's radius $R$ ). In such cases, universal potential energy formula $PE = -\frac{G M m}{r}$ must be used.

🛠️ Applications / Uses

▸
Hydroelectric power generation where water stored at a height possesses potential energy.
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Pendulums and roller coasters involving continuous conversion between kinetic and potential energy.

📄 Additional Information

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Option A ( $mgh$ ) represents the correct formula for gravitational potential energy near the Earth's surface.
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Option B ( $mg/h$ ) and Option D ( $m \times g$ ) are dimensionally incorrect for energy.
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Option C ( $m \times h$ ) lacks the acceleration due to gravity term.

📊 Diagram / Illustration

✅

A is correct — The gravitational potential energy of a body of mass $m$ at height $h$ is given by $mgh$ .

Core Concepts Used

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Gravitational Potential Energy Work Done Against Gravity Conservation of Energy

💡 EXAM TIP

Always verify dimensional consistency in mechanics problems: Potential Energy has dimensions $[M L^2 T^{-2}]$ , which matches $[M] \times [L T^{-2}] \times [L] = [M L^2 T^{-2}]$ for $mgh$ .

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