A floating/submerged body is always stable, if its centre of gravity

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

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 centre of percussion is below the centre of gravity of the body and is at a distance equal to

A

h / kG

B

h.kG

C

h2/kG

D

k2G/h

Centre of pressure in an immersed body is __________ the centre of gravity.

A

Above

B

Below

C

At

D

Either above or below; depends on the liquid density

The periodic time of a compound pendulum is __________ when the distance between the point of suspension and the center of gravity is equal to the radius of gyration of the body about its center of gravity.

A

Zero

B

Minimum

C

Maximum

D

None of these

The change in length due to a tensile or compressive force acting on a body is given by (where P = Tensile or compressive force acting on the body, $$l$$ = Original length of the body, A = Cross-sectional area of the body and E = Young's modulus for the material of the body)

A

$$\frac{{{\text{P}}l{\text{A}}}}{{\text{E}}}$$

B

$$\frac{{{\text{P}}l}}{{{\text{AE}}}}$$

C

$$\frac{{\text{E}}}{{{\text{P}}l{\text{A}}}}$$

D

$$\frac{{{\text{AE}}}}{{{\text{P}}l}}$$

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

A

Circle

B

Equilateral triangle

C

Rectangle

D

Right angled triangle

The centre of pressure for a vertically immersed surface lies at a distance equal to __________ the centre of gravity.

A

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }}{\text{ below}}$$

B

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }}{\text{ above}}$$

C

$$\frac{{{\text{A}}\overline {\text{x}} }}{{{I_{\text{G}}}}}{\text{ below}}$$

D

$$\frac{{{\text{A}}\overline {\text{x}} }}{{{I_{\text{G}}}}}{\text{ above}}$$

The centre of pressure acts __________ the centre of gravity of immersed surface.

A

At

B

Above

C

Below

D

None of these

If b is the wheel track of a vehicle and h is the height of centre of gravity above road surface, then to avoid overturning and lateral skidding on a horizontal curve, the centrifugal ratio should always be

A

Less than $$\frac{{\text{b}}}{{2{\text{h}}}}$$ and greater than co-efficient of lateral friction

B

Less than $$\frac{{\text{b}}}{{2{\text{h}}}}$$ and also less than co-efficient of lateral friction

C

Greater than $$\frac{{\text{b}}}{{2{\text{h}}}}$$ and less than co-efficient of lateral friction

D

Greater than $$\frac{{\text{b}}}{{2{\text{h}}}}$$ and also greater than coefficient of lateral friction

A floating/submerged body is always stable, if its centre of gravity

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