First slide

Moment of inertia

Question

An isosceles triangular piece is cut from a square plate of side l. The piece is one-fourth of the square and mass of the remaining plate is M. The moment of inertia of the plate about an axis passing through O and perpendicular to its plane is

Moderate

A

$\frac{M l^{2}}{6}$
B

$\frac{M l^{2}}{12}$
C

$\frac{M l^{2}}{24}$
D

$\frac{M l^{2}}{3}$

Solution

Mass of each of the four parts $= \frac{M}{3}$
Mass of the plate including the cut piece $= \frac{4 M}{3}$
Moment of inertia of the whole plate (including the cut piece) about the said axis $= (\frac{4 M}{3}) \frac{l^{2}}{6}$
Now moment of inertia of the remaining portion should be 3/4 of the above = $\frac{M l^{2}}{6} .$

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