Concepts Of Physics MCQ Edition [Volume 1]
- Exam
- Concepts Of Physics MCQ Edition [Volume 1]
- Subject
- Physics
- Chapter
- Circular Motion
Concepts Of Physics MCQ Edition [Volume 1] · Physics · Circular Motion
Three identical cars, A , B , and C , travel at the same speed...
Three identical cars, , , and , travel at the same speed across three bridges. Car drives on a flat bridge, car on a bridge that is convex upward, and car on a bridge that is concave upward. Let , , and denote the normal forces exerted by the cars on the bridges when they are at the center of the bridges. Which of the following statements is correct?
Options
- A is the largest of the three forces
- B is the largest of the three forces
- C
- D is the largest of the three forces
Correct answer
D. is the largest of the three forces
Step-by-step solution
For car moving on a flat bridge, the vertical acceleration is zero. The normal force is given by .
For car moving on a convex upward bridge, the centripetal acceleration is directed downwards towards the center of curvature. The equation of motion is , which gives .
For car moving on a concave upward bridge, the centripetal acceleration is directed upwards towards the center of curvature. The equation of motion is , which gives .
Comparing the three normal forces, we get .
Therefore, is the largest of the three forces.
For car moving on a convex upward bridge, the centripetal acceleration is directed downwards towards the center of curvature. The equation of motion is , which gives .
For car moving on a concave upward bridge, the centripetal acceleration is directed upwards towards the center of curvature. The equation of motion is , which gives .
Comparing the three normal forces, we get .
Therefore, is the largest of the three forces.