A smooth cylinder lying on its convex surface remains in __________ equilibrium.

A smooth cylinder lying on its convex surface remains

A

In stable equilibrium

B

In unstable equilibrium

C

In neutral equilibrium

D

Out of equilibrium

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. Consider the following statements: 1) The surface area of the sphere is √5 Times the curved surface area of the cone. 2) The surface area of the cube is equal to the curved surface area of the cylinder. Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2\

D

Neither 1 nor 2

A smooth cylinder lying on a __________ is in neutral equilibrium.

A

Curved surface

B

Convex surface

C

Horizontal surface

D

None of these

In convex learning problems where the loss function is convex, the preceding problem is also a convex optimisation problem.

A

False

B

True

A right circular cylinder is formed. A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?

A

154

B

308

C

462

D

616

The piston rod of a hydraulic cylinder exerts an operating force of 10kN. The allowable stress in the cylinder is 45N/mm². Calculate the thickness of the cylinder using Lame’s equation. Diameter of the cylinder is 40mm and pressure in cylinder is 10MPa.

A

2.05mm

B

4.2mm

C

5.07mm

D

None of the listed

The piston rod of a hydraulic cylinder exerts an operating force of 10kN. The allowable stress in the cylinder is 70N/mm². Calculate the thickness of the cylinder using Clavarinoe’s equation. Diameter of the cylinder is 240mm.μ=0.3 and pressure in cylinder is 15MPa.

A

35mm

B

30mm

C

27mm

D

None of the listed

If p₁, is the pressure of air entering the L.P. cylinder and p₂ is the pressure of air leaving the L.P. cylinder (or inter-cooler pressure), then the ratio of cylinder diameters for a single acting, two stage reciprocating air compressor with complete intercooling is given by (where D₁ = Diameter of L.P. cylinder and D₂ = Diameter of H.P. cylinder)

A

$$\frac{{{{\text{D}}_1}}}{{{{\text{D}}_2}}} = {{\text{p}}_1}{{\text{p}}_2}$$

B

$$\frac{{{{\text{D}}_1}}}{{{{\text{D}}_2}}} = \frac{{{{\text{p}}_1}}}{{{{\text{p}}_2}}}$$

C

$$\frac{{{{\text{D}}_1}}}{{{{\text{D}}_2}}} = \frac{{{{\text{p}}_2}}}{{{{\text{p}}_1}}}$$

D

None of these

When a body of mass M₁ is hanging freely and another of mass M₂ lying on a smooth inclined plane ($$\alpha $$) are connected by a light index tensile string passing over a smooth pulley, the acceleration of the body of mass M₁, will be given by

A

$$\frac{{{\text{g}}\left( {{{\text{M}}_1} + {{\text{M}}_2}\sin \alpha } \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}{\text{m/sec}}$$

B

$$\frac{{{\text{g}}\left( {{{\text{M}}_1} - {{\text{M}}_2}\sin \alpha } \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}{\text{m/se}}{{\text{c}}^2}$$

C

$$\frac{{{\text{g}}\left( {{{\text{M}}_2} + {{\text{M}}_1}\sin \alpha } \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}{\text{m/se}}{{\text{c}}^2}$$

D

$$\frac{{{\text{g}}\left( {{{\text{M}}_2} \times {{\text{M}}_1}\sin \alpha } \right)}}{{{{\text{M}}_2} - {{\text{M}}_1}}}{\text{m/se}}{{\text{c}}^2}$$

The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2,then what is the volume (in cm3) of cylinder?

A

247200

B

269500

C

312500

D

341800

A smooth cylinder lying on its convex surface remains in __________ equilibrium.

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