The forewheel of a tractor makes 120 revolutions more than the rear wheel in going 720m.if the diameter of the forewheel is doubled and the diameter of the rear wheel is increased by 1.5 times the present diameter then the forewheel makes 20 revolutions more than the rear wheel going same distance.find the circumference of each wheel.
Answers
☆In this question, we need to determine the circumference of each wheel of the tractor such that the fore wheel of a tractor makes 120 revolutions more than the rear wheel in going 720 meters. For this, we will establish the relation in accordance with the conditions given in the question and solve them simultaneously.
☆Let the diameter of the fore wheel of the tractor be
Let the diameter of forewheel is d m and rear wheel is D m.
☆To cover 720m, number of revolutions made by four wheel=720/circumference of four wheel
=720/πd
Similarly,To cover 720m,number of revolution made rear wheel =π/D
a/c to question,
720/πd-720/πD=120 revolutions
or,1/d-1/D=120π/720
or,1/d-1/D=π/6.....(1)
now forewheel diameter is doubled, so new diameter for forewheel=2d and diameter of rear wheel is increased by 1.5 times so new diameter of rearwheel=(3/2)D
now,to cover 720m,number of revolution of forewheel=720/π(2d)
To cover 720m,number of revolution of rear wheel=720/π(3/2)D
a/c to question,
720/π(2d)-720/π(3/2)D=20
For equation (1) and (2)
-1/2D+2/3D=π/12-π/36
D=3/π and d=2/π
So, circumference of forewheel=πd=2
circumference of rearwheel=πD=3