If the angular momentum of a rotating body about a fixed axis is increased by 10%. Its kinetic energ

If the angular momentum of a rotating body about a fixed axis is increased by 10%. Its kinetic energy will be increased by :-
(a) 10 % (b) 20 % (c) 21% (d) 5%
Description for the Problem: Effect of Angular Momentum on Kinetic Energy 🌪️🌀

This problem explores the relationship between *angular momentum* and *rotational kinetic energy**—a key concept in the study of rotational dynamics, especially for **IIT JEE and NEET* aspirants. Understanding how changes in angular momentum affect kinetic energy is essential for mastering physics topics related to rotational motion. Let's break it down step by step! 📘💡

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Problem Statement 🔍
If the angular momentum of a rotating body about a fixed axis is increased by \( 10\% \), by what percentage will its *kinetic energy* increase?

Options:
(a) \( 10\% \)
(b) \( 20\% \)
(c) \( 21\% \)
(d) \( 5\% \)

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Key Concepts to Understand 🧠

1. **Rotational Kinetic Energy**:
The kinetic energy of a rotating object is given by:
\[
K = \frac{L^2}{2I}
\]
where:
\( K \) is the rotational kinetic energy.
\( L \) is the angular momentum.
\( I \) is the moment of inertia (assumed constant since the axis is fixed).

2. **Relationship Between Angular Momentum and Kinetic Energy**:
Since the moment of inertia \( I \) is constant, the kinetic energy \( K \) is directly proportional to the *square* of the angular momentum \( L \).
This means:
\[
K \propto L^2
\]

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Step-by-Step Solution 📝

1. *Let the initial angular momentum be* \( L_0 \).
Initial kinetic energy:
\[
K_0 = \frac{L_0^2}{2I}
\]

2. **Increase the angular momentum by 10%**:
New angular momentum \( L_1 = 1.1 L_0 \)

3. *Calculate the new kinetic energy* with the increased angular momentum:
\[
K_1 = \frac{(L_1)^2}{2I} = \frac{(1.1 L_0)^2}{2I}
\]
\[
K_1 = \frac{1.21 L_0^2}{2I} = 1.21 K_0
\]

4. **Percentage increase in kinetic energy**:
\[
\text{Increase} = (K_1 - K_0) \times \frac{100}{K_0}
\]
\[
\text{Increase} = (1.21 K_0 - K_0) \times \frac{100}{K_0} = 0.21 \times 100 = 21\%
\]

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Explanation 🌟
When the angular momentum of a rotating body increases by *10%**, its kinetic energy increases by **21%* due to the quadratic relationship between angular momentum and kinetic energy. This problem highlights how even small changes in angular momentum can lead to significant increases in kinetic energy.

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Final Answer ✅
The correct answer is:
\[
\boxed{21\%}
\]

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Related Hashtags 📚
#AngularMomentum #RotationalKineticEnergy #PhysicsConcepts #IITJEE2025 #NEET2025 #PhysicsProblems #JEEPhysics #RotationalDynamics #ExamPreparation

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