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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, AA, BB, and CC, travel at the same speed across three bridges. Car AA drives on a flat bridge, car BB on a bridge that is convex upward, and car CC on a bridge that is concave upward. Let FAF_A, FBF_B, and FCF_C 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

  1. AFBF_B is the largest of the three forces
  2. BFAF_A is the largest of the three forces
  3. CFA=FB=FCF_A = F_B = F_C
  4. DFCF_C is the largest of the three forces

Correct answer

D. FCF_C is the largest of the three forces

Step-by-step solution

For car AA moving on a flat bridge, the vertical acceleration is zero. The normal force is given by FA=mgF_A = mg.

For car BB moving on a convex upward bridge, the centripetal acceleration is directed downwards towards the center of curvature. The equation of motion is mg−FB=mv2Rmg - F_B = \dfrac{mv^2}{R}, which gives FB=mg−mv2RF_B = mg - \dfrac{mv^2}{R}.

For car CC moving on a concave upward bridge, the centripetal acceleration is directed upwards towards the center of curvature. The equation of motion is FC−mg=mv2RF_C - mg = \dfrac{mv^2}{R}, which gives FC=mg+mv2RF_C = mg + \dfrac{mv^2}{R}.

Comparing the three normal forces, we get FC>FA>FBF_C > F_A > F_B.

Therefore, FCF_C is the largest of the three forces.
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