This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Helix upon a Cone”.

1. In a regular cone, the angle between base and slanting surface is 45 degrees and the base diameter is 100 mm. If a helix is to be built on such a cone with a pitch of 5. How many revolutions do the helix made in this cone?

a) 14.1

b) 18

c) 10

d) 20

View Answer

Explanation: Given angle between the base and slanting surface is 45 and the diameter of the base is 100 mm height of a cone is 100/2 x tan (45) =50. Pitch of helix is 5. Number of revolutions = total length of helix/ pitch of helix = 50/5 = 10.

2. In a regular cone, the angle between base and slanting surface is 60 degrees and the base diameter is 75 mm. If a helix is to be build on such a cone up to half of cones height with 6 revolutions in it. Pitch of the helix is?

a) 10.8

b) 5.4

c) 6.4

d) 12.9

View Answer

Explanation: Height of cone = diameter/2 x tan (angle) = 75/2 x tan (60) = 129.9mm/2= 64.95 mm. Half height is 32.475 mm. Helix made 6 revolution is this height so one revolution height is 32.475/6 = 5.4 mm which is the pitch of the helix.

3. A conical spring is to be designed with base diameter 100 mm and another end diameter 50 mm and pitch of spring is 5 mm to a height of 80 mm. How many revolutions are there in spring?

a) 15

b) 16

c) 17

d) 18

View Answer

Explanation: Whatever the end diameters of a conical spring the number of revolutions depends on the pitch and height of the spring. Number of revolutions = length of spring/pitch of helix = 80 mm/5 mm = 16.

4. Pitch of helix is 7 mm and the number of revolutions is 15. Length of spring is?

a) 100 mm

b) 10.5 cm

c) 110 mm

d) 12 cm

View Answer

Explanation: Length of spring = pitch of helix x number of revolutions, 7 mm x 15 = 0.7 cm x 15 = 10.5 cm = 105 mm. Length also includes a diameter of wire but here it is not mentioned and also not given the diameter of a wire.

5. Base diameter of conical helix is 80 mm, height of spring is 30 mm, angle between the base and slanting side of cone is 45 degrees and diameter of wire is 4 mm. What is the outer diameter at a top edge of spring?

a) 14

b) 24

c) 32

d) 18

View Answer

Explanation: Since the given angle is 45 degrees the max height of helix is equal to the radius of the base. Height given is 30 mm due to wire diameter the total helix height will be 26. 40 -26 =14 will be the radius of top end helix and due to the diameter of wire the outer diameter of top end is 14 x 2 + 4= 32 mm.

6. Mean diameter of conical spring is 100 mm, height of spring is 50 mm, angle between the base and slanting side of the cone is 45 degrees and diameter of the wire is 5 mm. What is the inner diameter at top edge of spring?

a) 10

b) 5

c) 20

d) 15

View Answer

Explanation: Since the given angle is 45 degrees the max height of spring is equal to the radius of the base. Height given is 50 mm. Due to a diameter of wire height of helix is 45 mm. 50-45 =5 will be the radius of top end helix and due to diameter of wire the inner diameter of top end is 5 x 2 -5= 5 mm.

7. Conical spring is also called a tapered spring.

a) True

b) False

View Answer

Explanation: Yes, conical spring is also called tapered spring since the diameter throughout the spring varies that is increases or decreases from one to other. Conical springs are better than cylindrical springs since conical springs can resist buckling effect.

8. The base diameter of a conical helix is 120 mm and other end diameter is 70 mm. The height of helix is 40 mm. What is the angle between the base and slanting side is?

a) 58 degrees

b) 60 degrees

c) 30 degrees

d) 45 degrees

View Answer

Explanation: Base radius= 60 mm. Other end radius = 35 mm. 60 mm– 35mm = 25 mm. height is 40 mm. tan (angle) = height/ base radius = 40 mm/25 mm = 1.6. Angle = tan-1(1.6) = 57.99 degrees approximately equals to 58 degrees.

9. The base diameter of a conical helix is 100 mm. The angle between the base and slanting side is 45 degrees. Pitch of helix is 5 mm. What is the height of helix and number of revolutions?

a) 50 mm, 10

b) 25 mm, 5

c) 30 mm, 7

d) 100 mm, 15

View Answer

Explanation: Base radius = 50 mm. Angle given is 45 degrees. Tan (angle) = height/ base, tan (45) = height/ 50, height = 50 x tan (45) = 50 mm, so at height of 50 mm the helix end. Number of revolutions = height/ pitch = 50 mm/ 5 mm = 10.

10. The base diameter of a conical helix is 100 mm and other end diameter is 80 mm. The height of helix is 50 mm. What is the angle between the base and slanting side is?

a) 58 degrees

b) 79 degrees

c) 89 degrees

d) 45 degrees

View Answer

Explanation: Base radius= 50 mm. Other end radius = 40 mm. 50 mm– 40mm = 10 mm. height is 50 mm. tan (angle) = height/ base radius = 50 mm/10 mm = 5. Angle = tan-1(5) = 78.69 degrees approximately equals to 79 degrees.

11. The base diameter of a conical helix is 80 mm. The angle between the base and slanting side is 60 degrees. Pitch of helix is 6 mm. What is the height of helix and number of revolutions?

a) 69.2 mm, 12

b) 39.2 mm, 6

c) 30 mm, 7

d) 80 mm, 12

View Answer

Explanation: Base radius = 40 mm. Angle given is 60 degrees. Tan (angle) = height/ base, tan (60) = height/ 40, height = 40 x tan (60) = 69.2 mm, so at height of 69.2 mm the helix end. Number of revolutions = height/ pitch = 69.2 mm/ 6 mm = 11.5 approximately 12.

12. Base diameter of a conical helix is 60 mm, height of spring is 30 mm, angle between the base and slanting side of cone is 45 degrees and diameter of wire is 3 mm. What is the outer diameter at the top edge of spring?

a) 14

b) 15

c) 30

d) 18

View Answer

Explanation: Since the given angle is 45 degrees the max height of helix is equal to radius of base. Height given is 30 mm due to wire diameter the total helix height will be 26. 30 -26 =4 will be the radius of top end helix and due to diameter of wire the outer diameter of top end is 4 x 2 + 3= 15 mm.

13. Base diameter of conical helix is 50 mm, height of helix is 30 mm, angle between the base and slanting side of cone is 60 degrees. What is the top end diameter of the helix?

a) 7.67 mm

b) 15.3 mm

c) 14.7 mm

d) 6.7 mm

View Answer

Explanation: Base radius = 25 mm. 30/tan (60) = difference between the base radius and top end radius = 17.3 mm. 25 mm- 17.3 mm = 7.67 mm (radius of top end radius). Diameter is 15.3 mm.

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