Related Questions

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 $$I\omega \omega {\text{P}}$$
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 $$\frac{{{\text{m}}{l^2}}}{{12}}$$
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
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
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
Mass moment of inertia of a uniform thin rod of mass (M) and length ($$l$$) about its mid-point and perpendicular to its length is
A $$\frac{2}{3}{\text{M}}{l^2}$$
B $$\frac{1}{3}{\text{M}}{l^2}$$
C $$\frac{3}{4}{\text{M}}{l^2}$$
D $$\frac{1}{{12}}{\text{M}}{l^2}$$
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 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 $$\frac{{{{\text{a}}^4}}}{{36}}$$
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 $$\frac{{\pi {{\text{d}}^4}}}{{36}}$$
A semicircular disc rests on a horizontal surface with its top flat surface horizontal and circular portion touching down. The coefficient of friction between semi circular disc and horizontal surface is µ. This disc is to be pulled by a horizontal force applied at one edge and it always remains horizontal. When the disc is about to start moving, its top horizontal force will
A Remain horizontal
B Slant up towards direction of pull
C Slant down towards direction of pull
D None of the above

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