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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

A car travels at a constant speed along a road, as shown in the...

A car travels at a constant speed along a road, as shown in the figure. The normal force exerted by the road on the car is NAN_A when the car is at point AA, and NBN_B when it is at point BB.
A car travels at a constant speed along a road, as shown in the figure. The normal force exerted by the road on the car

Options

  1. ANA=NBN_A = N_B
  2. BNA<NBN_A < N_B
  3. CNA>NBN_A > N_B
  4. Dthe relationship between NAN_A and NBN_B cannot be determined from the given information

Correct answer

B. NA<NBN_A < N_B

Step-by-step solution

At the highest point of a convex path, the net force towards the center of curvature provides the necessary centripetal force.

The equation of motion is:
mg−N=mv2Rmg - N = \dfrac{mv^2}{R}

Rearranging for the normal force NN, we get:
N=mg−mv2RN = mg - \dfrac{mv^2}{R}

From the given figure, the curve at point A is sharper than the curve at point B. This means the radius of curvature at A is smaller than that at B, i.e., RA<RBR_A < R_B.

Since the car travels at a constant speed vv, the term mv2R\dfrac{mv^2}{R} is larger for point A than for point B.

Therefore, mv2RA>mv2RB\dfrac{mv^2}{R_A} > \dfrac{mv^2}{R_B}

⇒mg−mv2RA<mg−mv2RB\Rightarrow mg - \dfrac{mv^2}{R_A} < mg - \dfrac{mv^2}{R_B}

⇒NA<NB\Rightarrow N_A < N_B
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