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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
The moment of inertia of a body about an axis passing through the center of mass is Icm. If the mass of the body is m, find the moment of inertia about an axis parallel to the center of mass and at a distance of R from it.
Let I1 be the moment of inertia about the centre of mass of a thick asymmetrical body. Let I2 be the moment of inertia about an axis parallel to I1. The distance between the two axes is ‘a’ & the mass of the body is ‘m’. Find the relation between I1 & I2.
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.
Mass moment of inertia of two arbitrary masses placed will be same as the mass moment inertia of the rigid body.
We sometimes use the moment caused by the force so as to determine the moment of inertia of the body. The moment is the cross product of which two vectors?
A torsional system with discs of moment of inertia $${I_1}$$ and $${I_2}$$ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is 'G'. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to
Theory of Machine mcq question image
Mass moment of inertia of a thin rod about its one end is ___________ the mass moment of inertia of the same rod about its mid-point
The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, 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.