A particle moves in a circular path of radius 2 m with a const... | General Science MCQ | Examoogle

General SciencePhysics: Motion

A particle moves in a circular path of radius 2 m with a constant speed of 4 m/s. Calculate the magnitude of centripetal acceleration.

2, $\text{m/s}^2$

4, $\text{m/s}^2$

8, $\text{m/s}^2$

16, $\text{m/s}^2$

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Motion

Option C

8, $\text{m/s}^2$

Quick Summary:

Centripetal acceleration is the rate of change of tangential velocity in a circular path. For a particle moving with a constant speed $v$ in a circle of radius $r$ , the magnitude is given by $a_c = \frac{v^2}{r}$ . Substituting the given values $v = 4\,\text{m/s}$ and $r = 2\,\text{m}$ results in $a_c = \frac{4^2}{2} = \frac{16}{2} = 8\,\text{m/s}^2$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of swinging a ball on a string; the tension in the string provides the constant inward pull required to keep the ball moving in a circle rather than flying off in a straight line.

🔢 Key Formulas

$a_c = \frac{v^2}{r}$ — Centripetal acceleration formula where $v$ is speed and $r$ is radius.

$a_c = \omega^2 r$ — Equivalent formula using angular velocity $\omega$ .

⚙️ Working Principle

In uniform circular motion, although the speed is constant, the direction of the velocity vector is continuously changing towards the center of the circle. This change in velocity over time necessitates an acceleration directed radially inward, known as centripetal acceleration, which is essential to maintain the circular trajectory.

📌 Key Points

▸
Centripetal acceleration is always directed toward the center of the circular path.
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Uniform circular motion implies that while the speed is constant, the velocity is variable due to continuous change in direction.
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The SI unit for centripetal acceleration is $\text{m/s}^2$ .

✅ Advantages

▸
Provides a direct measure of the kinematic requirement to maintain curvature.

❌ Disadvantages / Limitations

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Only applicable for particles moving along a path with a defined radius of curvature.

🛠️ Applications / Uses

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Calculation of banking angles for roads and railway tracks.
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Understanding the motion of satellites orbiting a planet.

📄 Additional Information

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If the speed $v$ were doubled, the centripetal acceleration would increase by a factor of 4 because it is proportional to $v^2$ .
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Option A is the result of $\frac{v}{r}$ , Option B is $v$ , and Option D is $v^2$ (incorrect dimensionality or formula application).

📊 Diagram / Illustration

✅

C is correct — The centripetal acceleration is calculated as $\frac{4^2}{2} = 8\,\text{m/s}^2$ .

Core Concepts Used

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Uniform Circular Motion Centripetal Acceleration Kinematics

💡 EXAM TIP

Always verify units before calculation; if radius were in cm, convert to meters first to ensure the result is in $\text{m/s}^2$ .

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