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

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 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

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 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 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 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

$$\frac{{3{\text{m}}{{\text{r}}^2}}}{5}$$

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 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 circular section about an axis perpendicular to the section is

A

$$\frac{{\pi {{\text{d}}^3}}}{{16}}$$

B

$$\frac{{\pi {{\text{d}}^3}}}{{32}}$$

C

$$\frac{{\pi {{\text{d}}^4}}}{{32}}$$

D

$$\frac{{\pi {{\text{d}}^4}}}{{64}}$$

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

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