M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is

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

$$\frac{{{\text{m}}{{\text{r}}^2}}}{8}$$

A thin spherical shell of internal diameter d is subjected to an internal pressure p. If V is the storage capacity of shell, then its diameter will be

A

$${\left( {\frac{{6{\text{V}}}}{\pi }} \right)^{\frac{1}{2}}}$$

B

$${\left( {\frac{{6{\text{V}}}}{\pi }} \right)^{\frac{1}{3}}}$$

C

$${\left( {\frac{{6{\text{V}}}}{\pi }} \right)^2}$$

D

$${\left( {\frac{{6{\text{V}}}}{\pi }} \right)^3}$$

A thin spherical shell of internal diameter d is subjected to an internal pressure p. If $${\sigma _{\text{t}}}$$ is the tensile stress for the shell material, then thickness of shell is equal to

A

$$\frac{{{\text{pd}}}}{{{\sigma _{\text{t}}}}}$$

B

$$\frac{{{\text{pd}}}}{{2{\sigma _{\text{t}}}}}$$

C

$$\frac{{{\text{pd}}}}{{3{\sigma _{\text{t}}}}}$$

D

$$\frac{{{\text{pd}}}}{{4{\sigma _{\text{t}}}}}$$

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 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 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

$$\frac{{\pi {{\text{d}}^4}}}{{36}}$$

Plane P take off at 2:00 am and flies at a constants speed of Xmph. Plane Q takes off at 3:30 am and flies the same forte as plane p but travels at a constant X, how many hours after 3:30 am will plane Q overtake plan P?

A

1.5x/y +0.5

B

2

C

4

D

5

A plate with an elliptical hole in the centre, with semi-major axis (a) perpendicular to the direction of loading and semi-minor axis (b) along the direction of loading, is subjected to a pull P. The maximum stress induced at the edge of the hole is equal to (where $$\sigma $$ = Stress for a plate with no hole i.e. nominal stress)

A

$$\sigma \left( {1 + \frac{{\text{b}}}{{2{\text{a}}}}} \right)$$

B

$$\sigma \left( {1 + \frac{{2{\text{a}}}}{{\text{b}}}} \right)$$

C

$$\sigma \left( {1 + \frac{{\text{b}}}{{3{\text{a}}}}} \right)$$

D

$$\sigma \left( {1 + \frac{{3{\text{a}}}}{{\text{b}}}} \right)$$

The M.I. of hollow circular section about a central axis perpendicular to section as compared to its M.I. about horizontal axis is

A

Same

B

Double

C

Half

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

M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is

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