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The moment of inertia of a planar square about a planar axis parallel to one side is 10kgm2. What is the moment of inertia about a diagonal?

Correct Answer: 10kgm2
Using perpendicular axis theorem we can say that sum of moment of inertia about two perpendicular axes will be the same as sum of moment of inertia about other 2 perpendicular axes. Let I1 be the moment of inertia about a diagonal, we can say: I1 + I1= 10 + 10 = 20kgm2 Or I1 =10kgm2.

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

The moment of inertia of a solid sphere is 10kgm2. What will be the moment of inertia of a very thin spherical shell of the same mass and radius as that of the solid sphere?

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$    A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.
Classical Mechanics mcq question image
The moment of inertia of the resulting body about Y-axis is

In order to have a connecting rod equally strong in buckling about X-axis and Y-axis, the moment of inertia about X-axis should be __________ the moment of inertia about Y-axis.

The parallel axis theorem can add any angle varied moment of inertias to give the perpendicular moment of inertia and it can be used in the determination of the moment of inertia about inclined axis.

A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded?

The length of each side of square A is increased by 100 percent to make square B. Again the length of each side of square B is increased by 50 percent to make square C. By what percent is the area of square C greater than the sum of the areas of square A and B?

A rectangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through center of gravity and parallel to base is ___________

A triangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through centroid and parallel to base is ______

The moment of inertia of a planar disc about a diameter is 8kgm2. What is the moment of inertia about an axis passing through its centre and perpendicular to the plane of disc?