Rotational In...

Rotational Inertia

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Q. A massless equilateral triangle

E F G

of side

a

(As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line

E X

perpendicular to

E G

in the plane of

E F G

\frac{N}{20} m a^{2}

where

N

is an integer. The value of

N

is .

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Q. Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

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Particles of masses 1 g, 2 g, 3 g, ........100 g are kept at the marks 1 cm, 2 cm, 3 cm, ........100 cm respectively on a metre scale. What is the moment of inertia of the system of particles about a perpendicular bisector of the metre scale?

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Q. Three point masses each of mass m are placed at the corners of an equilateral triangle of side a. The moment of inertia of system about the side AB is

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Q. The moment of inertia of HCl molecule about an axis passing through its centre of mass and perpendicular to the line joining the

H^{+}

and

C l^{-}

ions will be, if the interatomic distance is 1

o A

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Q. Four spheres, each of mass 'M' and radius 'r' are situated at the four corners of square of side 'R'. The moment of inertia of the system about an axis perpendicular to the plane of square and passing through its centre will be

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Two particles having masses $m_{1}$ and $m_{2}$ are situated in a plane perpendicular to line AB at a distance of $r_{1}$ and $r_{2}$ respectively as shown.

Find the moment of intertia about axis passing through centre of mass and perpendicular to line joining $m_{1}$ and $m_{2}$

$\frac{m_{1} m_{2}}{m_{1} + m_{2}}$ $(r_{1} + r_{2})^{2}$
$\frac{m_{1} m_{2}}{m_{1} + m_{2}}$ $(r_{1} - r_{2})^{2}$
$\frac{m_{1} m_{2}}{m_{1} + m_{2}}$ $(r_{1}^{2} + r_{2}^{2})$
$\frac{m_{1} m_{2}}{m_{1} + m_{2}}$ $(r_{1}^{2} + r_{2}^{2})$

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Two particles having masses $m_{1}$ and $m_{2}$ are situated in a plane perpendicular to line AB at a distance of $r_{1}$ and $r_{2}$ respectively as shown. Find the moment of inertia of the entire setup about an axis passing through system's centre of mass and perpendicular to line joining $m_{1}$ and $m_{2}$ .

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Four particles, each of mass $m$ , are kept at the four corners of a square of edge $a$ . What is the moment of inertia of the system about the line perpendicular to the plane of the square and passing through the centre of the square?

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The moment of Inertia of a solid cylinder of mass ' $M$ ' and radius $R$ about its Axis(as shown) is.

$M R^{2}$
$\frac{M R^{2}}{4}$
$\frac{M R^{2}}{2}$
$\frac{M R^{2}}{3}$

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