JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L / 2\) and radius \(R / 3\) carved from this cylinder has moment of inertia about its axis equals to \(I_2\). The ratio \(I_1 / I_2\) is _________ .
- A 162
- B 81
- C 54
- D 27
Answer & Solution
Correct Answer
(A) 162
Step-by-step Solution
Detailed explanation
Original mass (M) The removed mass (m) \(m=\rho \times \pi\left(\frac{ R }{3}\right)^2 \times \frac{ L }{2}\) \(=\frac{\rho \cdot \pi R ^2 L}{18}=\frac{ M }{18}\) \(I ^{\prime}=\frac{1}{2} \cdot \frac{ M }{18} \cdot \frac{ R ^2}{9}=\frac{1}{324} MR ^2\)…
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