Question

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre \(O\). Its angular momentum is \(L_A\) and \(L_B\) computed about points \(A\) and \(B\), respectively, where \(OB=2\times OA\). The value of \[ \frac{L_A}{L_B} \] is:

• A. \(2\)
• B. \(\frac14\)
• C. \(\frac12\)
• D. \(1\)

Hint:

Angular momentum depends on axis. For a fixed rotation axis, shifting origin along axis does not change angular momentum. Always identify the rotation axis first. Remember rigid body rotation properties.

Answer 1

The Correct Option is D

Concept:

• For a rigid body rotating about a fixed axis, angular momentum is independent of the choice of point on the axis.

• The disc rotates about the same vertical axis through \(O\).

• Hence angular momentum remains unchanged.

Step 1: Identify axis of rotation
The disc rotates about a fixed vertical axis through its centre.

Step 2: Compare angular momenta about different points
For points \(A\) and \(B\) on the same axis, \[ L_A=L_B \]

Step 3: Calculate ratio
\[ \frac{L_A}{L_B} = \frac{L_B}{L_B} =1 \]