Related Questions

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 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
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 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 thin spherical shell of mass m and radius r, about its diameter is
A $$\frac{{{\text{m}}{{\text{r}}^2}}}{3}$$
B $$\frac{{2{\text{m}}{{\text{r}}^2}}}{3}$$
C $$\frac{{2{\text{m}}{{\text{r}}^2}}}{5}$$
D $$\frac{{3{\text{m}}{{\text{r}}^2}}}{5}$$
একটি দৈর্ঘ্য এবং M ভরের রডের ভরকেন্দ্র দিয়ে যায় এমন একটি লম্ব অক্ষের সাপেক্ষে রডের জড়তার ভ্রামক কত হবে? (What is the moment of inertia of a rod of length L and mass M with respect to a perpendicular axis passing through it?)
A 12ML2
B 112ML2
C 13ML2
D 25ML2
The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft and $$I$$ = Mass moment of inertia of the disc attached at the end of a shaft)
A $$2\pi \sqrt {\frac{{\text{q}}}{I}} $$
B $$2\pi \sqrt {{\text{q}}I} $$
C $$\frac{1}{{2\pi }}\sqrt {\frac{{\text{q}}}{I}} $$
D $$\frac{1}{{2\pi }}$$
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
The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, $$\omega $$ = Angular speed of crank, r = Radius of crank, $$\theta $$ = Angle of inclination of crank with the line of stroke and n = Ratio of the length of connecting rod to radius of crank)
A $${\text{m}}{\omega ^2}{\text{r}}\sin \theta $$
B $${\text{m}}{\omega ^2}{\text{r}}\cos \theta $$
C $${\text{m}}{\omega ^2}{\text{r}}\frac{{\sin 2\theta }}{{\text{n}}}$$
D $${\text{m}}{\omega ^2}{\text{r}}\frac{{\cos2\theta }}{{\text{n}}}$$

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