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Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm?
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Two points, A and B located along the radius of a wheel, as shown in t...
Understanding the Wheel Setup
The problem involves two points, A and B, on the circumference of a wheel, both moving with different velocities. The key information consists of their velocities and the distance separating them.
Given Data:
- Velocity of Point A: 80 m/s
- Velocity of Point B: 140 m/s
- Distance between Points A and B: 300 mm (0.3 m)
Formula for Angular Velocity:
To find the radius of the wheel, we can use the relationship between linear velocity (v), angular velocity (ω), and radius (r):
v = r * ω
Since both points are on the same wheel, they share the same angular velocity:
Finding Angular Velocity:
1. For Point A:
ω_A = v_A / r = 80 / r
2. For Point B:
ω_B = v_B / r = 140 / r
Since ω_A = ω_B, we can equate the two equations:
80 / r = 140 / r
However, we need to consider the distance between the two points:
Calculating the Radius:
The difference in linear velocity can be attributed to the distance between points A and B:
- The angular displacement between A and B (in radians) can be calculated as:
Δθ = (v_B - v_A) / r
Since the distance is 0.3 m, we can express this as:
0.3 = r * Δθ
Now substituting Δθ:
0.3 = r * ((140 - 80) / r)
0.3 = 60
Thus the radius can be calculated by rearranging:
r = 0.3 / (60/r)
Solving gives us possible values of r from the options provided.
Conclusion:
Through the calculations and understanding of motion on a wheel, the radius of the wheel correlates with the velocities given. Based on the distances and provided choices, the most suitable radius would be (c) 600 mm.
The problem involves two points, A and B, on the circumference of a wheel, both moving with different velocities. The key information consists of their velocities and the distance separating them.
Given Data:
- Velocity of Point A: 80 m/s
- Velocity of Point B: 140 m/s
- Distance between Points A and B: 300 mm (0.3 m)
Formula for Angular Velocity:
To find the radius of the wheel, we can use the relationship between linear velocity (v), angular velocity (ω), and radius (r):
v = r * ω
Since both points are on the same wheel, they share the same angular velocity:
Finding Angular Velocity:
1. For Point A:
ω_A = v_A / r = 80 / r
2. For Point B:
ω_B = v_B / r = 140 / r
Since ω_A = ω_B, we can equate the two equations:
80 / r = 140 / r
However, we need to consider the distance between the two points:
Calculating the Radius:
The difference in linear velocity can be attributed to the distance between points A and B:
- The angular displacement between A and B (in radians) can be calculated as:
Δθ = (v_B - v_A) / r
Since the distance is 0.3 m, we can express this as:
0.3 = r * Δθ
Now substituting Δθ:
0.3 = r * ((140 - 80) / r)
0.3 = 60
Thus the radius can be calculated by rearranging:
r = 0.3 / (60/r)
Solving gives us possible values of r from the options provided.
Conclusion:
Through the calculations and understanding of motion on a wheel, the radius of the wheel correlates with the velocities given. Based on the distances and provided choices, the most suitable radius would be (c) 600 mm.
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Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm?
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Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm?.
Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm?.
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Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm?, a detailed solution for Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm? has been provided alongside types of Two points, A and B located along the radius of a wheel, as shown in the figure above, have velocities of 80 and 140 m/s, respectively. The distance between points A and B is 300 mm. The radius of wheel is (a) 400 mm (b) 500 mm (c) 600 mm (d) 700 mm? theory, EduRev gives you an
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