Comparative Scale
Comparative scales:
These are the scales having the same R.F. but graduated to read different units.
These scales may be plain scales or Diagonal scales and may be constructed separately or one above the other.
Problems on comparative scales
1 ] A distance of 40 miles is represented by a line 8 cm long. Construct a plain scale to read kilometers up to 120 km(1 m=1.609 km)
SOLUTION STEPS:
Scale of miles:
40 miles are represented = 8 cm
80 miles = 16 cm
R.F = 8/40 x 1609 x 1000 x 100
= 1/8,04,500
Construction:
Take a line 16 cm long and divide it into 8 parts. Each will represent 10 miles. Subdivide the first part and each sub-division will measure a single mile.
Scale of km:
Length of scale = 1/8,04,500 x 120 x 1000 x 100
= 14.90 cm
Construction:
On the top line of the scale of miles cut off a distance of 14.90 cm and divide it into 12 equal parts. Each part will represent 10 km. Subdivide the first part into 10 equal parts. Each subdivision will show a single km.
COMPARATIVE SCALE SHOWING MILES AND KILOMETERS
2 ] A motor car is running at a speed of 60 kph. On a scale of RF=1/4,00,000 shows the distance traveled by car in 47 minutes.
SOLUTION STEPS:
Scale of km.
length of scale =RF x 60 km
= 1/4,00,000 x 60 x 105
=15 cm.
Construction:
Drew a line 15 cm long and divide it into 6 equal parts. (each part will represent 10 km.) subdivide 1st part in 0 equal subdivisions. (each will represent 1 km.)
Time Scale:
The same 15 cm line will represent 60 minutes. Construct the scale similar to the distance scale. It will show a minimum of 1-minute & max.60 min.
COMPARATIVE SCALE SHOWING MILES AND KILOMETERS
3 ] A car is traveling at a speed of 60 km per hour. A 4 cm long line represents the distance traveled by the car in two hours. Construct a suitable comparative scale of up to 10 hours. The scale should bee able to read the distance traveled in one minute. Show the time required to cover 476 km and also the distance in 4 hours and 24 minutes.
SOLUTION:
4 cm line represent distance in two hours, means for 10 hours scale, 20 cm long line is required, as the length of the scale. This length of scale will also represent 600 km. (as it a distance traveled in 10 hours)
CONSTRUCTION:
Distance scale(km)
- Drew a line 20 cm long. Divide it in TEN equal parts. (Each will show 60 km)
- sub-divide 1 st part in six subdivisions. (Each will represent 10 km)
- At the left-hand end of the line, drew a vertical line and on it step-off 10 equal division of any length. And complete the diagonal scale to read a minimum of ONE km.
Time scale:
- Drew a line 20 cm long. Divide it in TEN equal parts. (Each will show 1 hour) sub-divide 1st part in SIX subdivisions. (Each will represent 10 minutes )
- At the left hand of the line, drew a vertical line and on it step-off 10 equal divisions of any length. And complete the diagonal scale to read minimum ONE minute.
