Angular Momentum of Copper and Aluminium Spheres – Rankers Physics

Angular Momentum and Conservation of Angular Momentum: Practice Problem & Solution

Assertion (A): A solid copper and solid aluminium sphere of same masses are spinning about their axes with same angular velocities copper sphere has more angular momentum than aluminium. Reason (R): Both copper and aluminium sphere have same radius.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Angular Momentum and Conservation of Angular Momentum. Understanding the underlying formula is key to arriving at the correct answer below:

Angular momentum \( L = I\omega = \frac{2}{5} MR^2 \omega \). If mass (M) and angular velocity (\( \omega \)) are the same, L depends on \( R^2 \). Copper is denser than aluminium (\( \rho_{Cu} > \rho_{Al} \)). For the same mass, \( V_{Cu} < V_{Al} \), implying \( R_{Cu} < R_{Al} \). Therefore, \( L_{Cu} < L_{Al} \), making (A) false.

Also, \( R_{Cu} < R_{Al} \), so (R) is false. Both (A) and (R) are false.

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