All India Mechanical Engineering Group

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)
For... moremula 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.