Moment Of Inertia Of A Rod MCQ - Practice Questions & Answers

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A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is:

$\frac{2 g}{3 L}$

$\frac{3 g}{2 L}$

$\frac{g}{L}$

$\frac{2 g}{L}$

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Moment of inertia of a Rod

Let I=Moment of inertia of a ROD about an axis through its center and perpendicular to it

To calculate I (Moment of inertia of rod)

Consider a uniform straight rod of length L, mass M and having center C

mass per unit length of the rod = $λ = \frac{M}{L}$

Take a small element of mass dm with length dx at a distance x from point C.

$\begin{aligned} d m & = λ \cdot d x = \frac{M}{L} \cdot d x \\ \Rightarrow d I & = x^{2} d m \end{aligned}$

Now integrate this dl between the limits $x = - \frac{L}{2}$ to $\frac{L}{2}$

$I = \int d I = \int x^{2} d m = \int_{\frac{- L}{2}}^{\frac{L}{2}} \frac{M}{L} x^{2} * d x = \frac{M}{L} \int_{\frac{- L}{2}}^{\frac{L}{2}} x^{2} d x = \frac{M L^{2}}{12}$

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Moment Of Inertia Of A Rod MCQ - Practice Questions with Answers

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