The moment of inertia of a uniform horizontal | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The moment of inertia of a solid cylinder about an axis passing through its center of mass and perpendicular to its longitudinal axis is given by:

Vedclass · Accepted Answer

$\frac{49 M R^2}{4}$

Vedclass · Answer

(D) The moment of inertia of a solid cylinder about an axis passing through its center of mass and perpendicular to its longitudinal axis is given by:$I_{XY} = M \left( \frac{l^2}{12} + \frac{R^2}{4} \right)$Using the parallel axis theorem, the moment of inertia $I_{AB}$ about an axis passing through its edge and perpendicular to the longitudinal axis is:$I_{AB} = I_{XY} + M \left( \frac{l}{2} \right)^2$Substituting the expression for $I_{XY}$:$I_{AB} = M \left( \frac{l^2}{12} + \frac{R^2}{4} \right) + M \frac{l^2}{4}$$I_{AB} = M \left( \frac{l^2}{3} + \frac{R^2}{4} \right)$Given that the length $l = 6R$, we substitute this into the equation:$I_{AB} = M \left[ \frac{(6R)^2}{3} + \frac{R^2}{4} \right]$$I_{AB} = M \left[ \frac{36R^2}{3} + \frac{R^2}{4} \right]$$I_{AB} = M \left[ 12R^2 + \frac{R^2}{4} \right]$$I_{AB} = M \left( \frac{48R^2 + R^2}{4} \right) = \frac{49 M R^2}{4}$

The moment of inertia of a uniform horizontal solid cylinder of mass $M$ about an axis passing through its edge and perpendicular to the axis of the cylinder, when its length is $6$ times its radius $R$, is:

Similar Questions

The rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

The moment of inertia of a uniform circular disc about a diameter is $I$. What is its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim (in $I$)?

From a uniform circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc is

According to the parallel axis theorem,$I = I_C + Mx^2$. Which of the following graphs of $I$ versus $x$ is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module