JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
Let the moment of inertia of a hollow cylinder of length \(30\, cm\) (inner radius \(10\, cm\) and outer radius \(20\, cm\)), about its axis be \(I\). The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also \(I\), is ......... \(cm\).
- A \(12\)
- B \(16\)
- C \(14\)
- D \(18\)
Answer & Solution
Correct Answer
(B) \(16\)
Step-by-step Solution
Detailed explanation
\(r = 10 cm\) mass per unit \(R = 20 cm\) area \(Mass = m\) \(\sigma = \frac{m}{{\pi \left( {{R^2} - {r^2}} \right)}}\) Consider an element of radius \(x\) and thickness \(dx\) Mass of element \(dm =\) \(\sigma \,2\pi \times x\left( {dx} \right)\) Moment of inertia of element,…
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