Related Questions

A spherical body is symmetrical about its perpendicular axis. According to Routh's rule, the moment of inertia of a body about an axis passing through its centre of gravity is (where, M = Mass of the body and S = Sum of the squares of the two semi-axes.)
A $$\frac{{{\text{MS}}}}{3}$$
B $$\frac{{{\text{MS}}}}{4}$$
C $$\frac{{{\text{MS}}}}{5}$$
D None of these
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.
A Equal to
B Twice
C Three times
D Four times
The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is
A $$\frac{1}{4}$$
B $$\frac{1}{2}$$
C $$\frac{3}{4}$$
D $$2$$
The moment of inertia of a thin rod of mass 'm' and length '$$l$$', about an axis through its centre of gravity and perpendicular to its length is
A $$\frac{{{\text{m}}{l^2}}}{4}$$
B $$\frac{{{\text{m}}{l^2}}}{6}$$
C $$\frac{{{\text{m}}{l^2}}}{8}$$
D $$\frac{{{\text{m}}{l^2}}}{{12}}$$
The moment of inertia of a square of side (a) about an axis through its center of gravity is
A $$\frac{{{{\text{a}}^4}}}{4}$$
B $$\frac{{{{\text{a}}^4}}}{8}$$
C $$\frac{{{{\text{a}}^4}}}{{12}}$$
D $$\frac{{{{\text{a}}^4}}}{{36}}$$
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
A Same as
B Twice
C Thrice
D Four times
The moment of inertia of a thin disc of mass ‘m’ and radius ‘r’, about an axis through its center of gravity and perpendicular to the plane of the disc is
A $$\frac{{{\text{m}}{{\text{r}}^2}}}{2}$$
B $$\frac{{{\text{m}}{{\text{r}}^2}}}{4}$$
C $$\frac{{{\text{m}}{{\text{r}}^2}}}{6}$$
D $$\frac{{{\text{m}}{{\text{r}}^2}}}{8}$$
The moment of inertia of a circular lamina of diameter ‘d’, about an axis perpendicular to the plane of the lamina and passing through its centre, is
A $$\frac{{\pi {{\text{d}}^4}}}{{12}}$$
B $$\frac{{\pi {{\text{d}}^4}}}{{16}}$$
C $$\frac{{\pi {{\text{d}}^4}}}{{24}}$$
D $$\frac{{\pi {{\text{d}}^4}}}{{32}}$$
E $$\frac{{\pi {{\text{d}}^4}}}{{36}}$$
Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its vertex and parallel to the base, is __________ than that passing through its C.G. and parallel to the base.
A Nine times
B Six times
C Four times
D Two times
A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$  = Angular velocity of precession of the axis of spin)
A $$\frac{1}{2}I{\omega ^2}$$
B $$I{\omega ^2}$$
C $$\frac{1}{2}I\omega \omega {\text{P}}$$
D $$I\omega \omega {\text{P}}$$

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