This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Construction of Spiral”.

1. Which of the following represents an Archemedian spiral?

a) Tornado

b) Cyclone

c) Mosquito coil

d) Fibonacci series

View Answer

Explanation: Archemedian spiral is a curve traced out by a point moving in such a way that its movement towards or away from the pole is uniform with the increase of the vectorial angle from the starting line. It is generally used for teeth profiles of helical gears etc.

2. Steps are given to draw normal and tangent to an archemedian curve. Arrange the steps, if O is the center of curve and N is point on it.

i. Through N, draw a line ST perpendicular to NM. ST is the tangent to the spiral.

ii. Draw a line OM equal in length to the constant of the curve and perpendicular to NO.

iii. Draw the line NM which is normal to the spiral.

iv. Draw a line passing through the N and O which is radius vector.

a) ii, iv, i, iii

b) i, iv, iii, ii

c) iv, ii, iii, i

d) iii, i, iv, ii

View Answer

Explanation: The normal to an archemedian spiral at any point is the hypotenuse of the right angled triangle having the other two sides equal in length to the radius vector at that point and the constant of the curve respectively.

3. Which of the following does not represents an Archemedian spiral?

a) Coils in heater

b) Tendrils

c) Spring

d) Cyclone

View Answer

Explanation: Tendrils are a slender thread-like structures of a climbing plant, often growing in a spiral form. For cyclones the moving point won’t have constant velocity. The archemedian spirals have a constant increase in the length of a moving point. Spring is a helix.

4. Match the following. Given points are about spirals.

1. | The point about which the line rotates is called ___________ | i. | Radius vector |

2. | The line joining any point on the curve with the pole is called ________ | ii. | Convolution |

3. | Each complete revolution of the spiral is termed as ___________ | iii. | Vectorial angle |

4. | Angle between radius vector and the line in its initial position is called _____ | iv. | Pole |

a) 1, i; 2, ii; 3, iii; 4, iv

b) 1, ii; 2, iii; 3, i; 4, iv

c) 1, iv; 2, i; 3, ii; 4, iii

d) 1, ii; 2, iv; 3, iii; 4, i

View Answer

Explanation: The line joining any point on the curve with the pole is called radius vector. Angle between radius vector and the line in its initial position is called vectorial angle. Each complete revolution of the spiral is termed as convolutions. A spiral may make any number of convolutions before it reaches the pole.

5. Match the following.

1. | Tendrils | i. | Helix |

2. | Spring | ii. | Archemedian spiral |

3. | Mosquito coil | iii. | Fibonacci spiral |

4. | Cyclone | iv. | Lituus spiral |

a) 1, i; 2, ii; 3, iii; 4, iv

b) 1, ii; 2, iii; 3, i; 4, iv

c) 1, ii; 2, iv; 3, iii; 4, i

d) 1, iv; 2, i; 3, ii; 4, iii

View Answer

Explanation: These are general structures we used to see in our daily life which have certain particular names when comes to spirals. Since some of them are natural structures they may obey or disobey the perfect spiral shapes but looks alike to particular spirals.

6. Match the following, given are the equations of different types of spirals.

1. | Lituus spiral | i. | r = a + b. Ѳ |

2. | Logarithmic spiral | ii. | r=Ɵ |

3. | Archemedian spiral | iii | r= a e^{bӨ} |

4. | Fermat’s spiral | iv. | r=Ɵ^{1/2} |

a) 1, i; 2, ii; 3, iii; 4, iv

b) 1, ii; 2, iii; 3, i; 4, iv

c) 1, ii; 2, iv; 3, iii; 4, i

d) 1, iv; 2, i; 3, ii; 4, iii

View Answer

Explanation: Given are equations in polar co-ordinate system, which have r (radius) and theta Ɵ (angle). Where a, b are some constants and e represents exponential function.

7. Logarithmic spiral is also called Equiangular spiral.

a) True

b) False

View Answer

Explanation: The logarithmic spiral is also known as equiangular spiral because of its property that the angle which the tangent at any point on the curve makes with the radius vector at that point is constant. The values of vectorial angles are in arithmetical progression.

8. In logarithmic Spiral, the radius vectors are in arithmetical progression.

a) True

b) False

View Answer

Explanation: In the logarithmic Spiral, the values of vectorial angles are in arithmetical progression and radius vectors are in the geometrical progression that is the lengths of consecutive radius vectors enclosing equal angles are always constant.

9. The mosquito coil we generally see in house hold purposes and heating coils in electrical heater etc are generally which spiral.

a) Logarithmic spiral

b) Equiangular spiral

c) Fibonacci spiral

d) Archemedian spiral

View Answer

Explanation: Archemedian spiral is a curve traced out by a point moving in such a way that its movement towards or away from the pole is uniform with the increase of the vectorial angle from the starting line. The use of this curve is made in teeth profiles of helical gears, profiles of cam etc.

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