JNTU
JNTU B.Tech I Year ENGINEERING GRAPHICS Previous Question Paper (May - 2019 - R18)
Answer all five questions. All questions carry equal marks.
Main
Construct a conic when the distance of its focus from the directrix is equal to 50 mm and its eccentricity is 3/4. Measure its major and minor axes. Draw a tangent at any point on the curve. What is the distance between the foci? [15]
Answer
To construct the conic section with eccentricity e = 3/4 (which is less than 1, identifying it as an ellipse) and a focus-directrix distance (VF) of 50 mm, follow these steps:
- Draw a vertical line as the directrix. Draw a horizontal line (the axis) perpendicular to the directrix.
- Mark the focus F on the axis at a distance of 50 mm from the directrix.
- Divide the distance VF into 7 equal parts (since 3+4=7). The vertex V is located at the 3rd division from the directrix.
- Mark the vertex V such that VF = 3 units and the distance from the directrix to V is 4 units.
- To find the center and axes, construct a perpendicular at V to the axis. Measure a distance VE on this perpendicular such that VE = VF. Draw a line from the directrix intersection through E to define the eccentricity slope.
- Locate points on the curve by drawing vertical lines at intervals along the axis. For each line, measure the distance x from the directrix, calculate the radius r = e × x, and strike arcs from the focus F to intersect the vertical line.
- Connect the points to complete the ellipse.
Measurements:
- The major axis is the distance between the two vertices of the ellipse, typically measuring approximately 171.4 mm.
- The minor axis is determined by the double ordinate passing through the center, measuring approximately 113.4 mm.
Tangent Construction:
- Select any point P on the ellipse. Join PF. Draw a line through F perpendicular to PF, meeting the directrix at point T. The line passing through T and P is the required tangent to the curve at point P.
Distance between Foci:
The distance between the two foci (2c) is calculated using the relationship between the eccentricity and the axes:
Given the construction parameters, the distance between the two foci is approximately 128.5 mm.
Distance between Delhi and Chennai is 1800 km. On a railway map, it is represented by 36 cm length. Calculate the RF. Construct a diagonal scale to read up to a single kilometer. Mark on it the following distances 76 km and 593 km.
Answer
The Representative Fraction (RF) is the ratio of the drawing length to the actual length. Given that 36 cm represents 1800 km:
To construct the diagonal scale:
- Determine the Length of Scale (LOS). Assuming a maximum length of 600 km, LOS = RF × Max Length = (1/5,000,000) × 600 × 10^5 cm = 12 cm.
- Draw a line 12 cm long and divide it into 6 equal parts, each representing 100 km.
- Subdivide the first part into 10 divisions to represent 10 km each.
- Use the diagonal principle to further subdivide the height into 10 divisions to represent 1 km units.
- To mark 76 km: Locate 70 km on the main scale and move 6 units up the diagonal.
- To mark 593 km: Locate 500 km on the main scale, 90 km on the primary subdivisions, and 3 units up the diagonal.
Construct a cycloid having a rolling circle of 50 mm diameter. Also draw a tangent and normal at any point P on the curve.
Answer
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A line AB of 70 mm long has its end A at 10 mm above HP and 15 mm in front of VP. Its front view and top view measure 50 mm and 60 mm respectively. Draw the projections of the line and determine its inclinations with HP and VP. [15]
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A regular pentagon of 30 mm edges has an edge on the HP and perpendicular to the VP. The corner opposite to the edge on the HP is 30 mm above the HP. Show the projections of the pentagon. Determine the inclination of the surface with the HP. [15]
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A cube of edge 50 mm is resting on HP on one of its corners with a solid diagonal perpendicular to VP. Draw the projections of the cube. [15]
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A cylinder of base diameter 60 mm and axis 70 mm long is resting on its base in the HP. It is cut by two auxiliary inclined planes which make angles of 60° and 45° to HP and pass through the top end of the axis. Draw its sectional top view and true shape of the section. [15]
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A cone, base 50 mm diameter and axis 60 mm long, rests with its base on HP. A section plane perpendicular to VP and inclined at 45° to HP bisects the axis of the cone. Draw the development of lateral surface of the remaining portion of the cone. [15]
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A square prism of base side 60 mm rests on one of its ends on the HP with the base sides equally inclined to the VP. It is penetrated fully by another square prism of base side 45 mm with the base side equally inclined to the HP. The axes intersect at right angles. The axis of the penetrating prism is parallel to both the HP and the VP. Draw the projections of the prisms and show the lines of intersection. [15]
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Prepare an isometric view of the object shown in figure 1. All the dimensions are in mm only. [15]
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Draw the front view, top view and side view of figure 2. All dimensions are in mm only. [15]
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