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(B) The moment of inertia $I$ of a system of point masses about an axis is given by $I = \sum m_i r_i^2$,where $m_i$ is the mass and $r_i$ is the perp

Vedclass · Accepted Answer

$1.04$

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(B) The moment of inertia $I$ of a system of point masses about an axis is given by $I = \sum m_i r_i^2$,where $m_i$ is the mass and $r_i$ is the perpendicular distance from the axis of rotation $P$.From the figure,the distances of the masses from axis $P$ are:- Two $5 \ kg$ masses are at a distance of $0.2 \ m$ from axis $P$.- Two $2 \ kg$ masses are at a distance of $(0.2 \ m + 0.2 \ m) = 0.4 \ m$ from axis $P$.Calculating the total moment of inertia $I_P$:$I_P = (5 \ kg 	imes (0.2 \ m)^2) + (5 \ kg 	imes (0.2 \ m)^2) + (2 \ kg 	imes (0.4 \ m)^2) + (2 \ kg 	imes (0.4 \ m)^2)$$I_P = 2 	imes (5 	imes 0.04) + 2 	imes (2 	imes 0.16)$$I_P = 2 	imes (0.2) + 2 	imes (0.32)$$I_P = 0.4 + 0.64$$I_P = 1.04 \ kg \cdot m^2$.

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

Similar Questions

Assertion $(A)$: The moment of inertia of a steel sphere is larger than the moment of inertia of a wooden sphere of the same radius.
Reason $(R)$: Moment of inertia is independent of the mass of the body.
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In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?

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Write the practical uses of moment of inertia.

$A$ solid sphere $A$ is rotating about an axis $PQ$. If the radius of the sphere is $5 \, cm$ and the distance of its center from the axis $PQ$ is $10 \, cm$,then its radius of gyration about $PQ$ will be $\sqrt{x} \, cm$. The value of $x$ is $................$.

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