The Question is from neet-physics kinetic-theory-gases , and it was created by the author Mr. ANIL KUMAR.G

Question

A rigid diatomic molecule rotates about an axis perpendicular to the line joining the atoms.  If the moment of inertia is $I$ and the angular momentum is $L$, what is the rotational kinetic energy of the molecule?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Rotational Kinetic Energy
 **Related Topics**: Angular Momentum, Moment of Inertia
 **Prerequisites**: Understanding of rotational motion,  relationship between angular momentum, moment of inertia, and angular velocity.
## SOLUTION PATHWAY
**Given Information**:
  Moment of inertia, $I$
  Angular momentum, $L$
**Method & Steps**:
 1. Relate angular momentum and angular velocity.
  Reasoning: Angular momentum ($L$) is the product of moment of inertia ($I$) and angular velocity ($\omega$).
  Formula/Rule: $L = I\omega$
 2. Express rotational kinetic energy in terms of $I$ and $\omega$.
  Working: Rotational kinetic energy ($K$) is given by $K = \frac{1}{2}I\omega^2$.  We can substitute $\omega = \frac{L}{I}$ from step 1.
  Key Point:  Substituting $\omega$ eliminates the need for $\omega$ in the final expression.
 3. Substitute and simplify to find the rotational kinetic energy.
  Result: $K = \frac{1}{2}I(\frac{L}{I})^2 = \frac{L^2}{2I}$
  Verification: The units are consistent: $[K] = \frac{[L]^2}{[I]} = \frac{(kg \cdot m^2/s)^2}{kg \cdot m^2} = kg \cdot m^2/s^2 = J$ (Joules)
 ## OPTION ANALYSIS
A :x: $L^2/I$: This is incorrect because it misses the factor of 1/2 in the kinetic energy formula.
B ✓: $L^2/2I$: This is the correct expression for rotational kinetic energy in terms of angular momentum and moment of inertia.
C :x: $I\omega^2$: This is the formula for rotational kinetic energy, but it's not expressed in terms of $L$ and $I$ as required.
D :x: $I\omega$: This represents angular momentum, not kinetic energy.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing angular momentum with rotational kinetic energy: Remember that kinetic energy is proportional to the square of the angular velocity.
  2.Incorrectly using the formula for rotational kinetic energy: Carefully substitute the correct values and simplify.
 **Quick Tips**:
  1.Remember the basic formula for rotational kinetic energy: $K = \frac{1}{2}I\omega^2$.
  2.Understand the relationship between angular momentum, moment of inertia, and angular velocity: $L = I\omega$

Mr. ANIL KUMAR.G · Answer

$L^2 / I$

Mr. ANIL KUMAR.G · Answer

The correct Option is "$L^2 / 2I$"

Mr. ANIL KUMAR.G · Answer

$I\omega^2$

Mr. ANIL KUMAR.G · Answer

$I\omega$

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