The centre of gravity of a plane lamina will not be at its geometrical centre if it is a

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

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

The C.G. of a plane lamina will not be at its geometrical centre in the case of a

A

Right angled triangle

B

Equilateral triangle

C

Square

D

Circle

The centre of gravity of a uniform lamina lies at

A

The centre of heavy portion

B

The bottom surface

C

The midpoint of its axis

D

All of the above

The center of gravity of a uniform lamina lies at

A

The center of heavy portion

B

The bottom surface

C

The mid point of its axis

D

All of the above

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

At the instantaneous center, the velocity of the moving lamina at any instant is

A

Zero

B

Maximum

C

Minimum

D

Varying

Which of the following could be lamina proximately the thickness of laminations of a D.C. machine?

A

0.005 mm

B

0.05 mm

C

0.5 m

D

5 m

A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be

A

$$\frac{{{\text{r}}\left( {\pi + 0.25} \right)}}{{\pi - 0.5}}$$

B

$$\frac{{{\text{r}}\left( {\pi - 0.5} \right)}}{{\pi + 0.25}}$$

C

$$\frac{{{\text{r}}\left( {\pi - 0.25} \right)}}{{\pi - 0.5}}$$

D

$$\frac{{{\text{r}}\left( {\pi + 0.25} \right)}}{{\pi + 0.5}}$$

A body of weight 'W' is required to move up on rough inclined plane whose angle of inclination with the horizontal is 'α'. The effort applied parallel to the plane is given by (where μ = tanφ = Coefficient of friction between the plane and the body.)

A

P = W tanα

B

P = W tan (α + φ)

C

P = W (sinα + μcosα)

D

P = W (cosα + μsinα)

A submerged body is said to be in a stable equilibrium, if its centre of gravity __________ the centre of buoyancy.

A

Coincides with

B

Lies below

C

Lies above

D

None of these

The centre of gravity of a plane lamina will not be at its geometrical centre if it is a

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