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NEET PHYSICSLAWS OF MOTIONEasy

Question

A car of mass 1000 kg1000 \text{ kg} negotiates a banked curve of radius 90 m90 \text{ m} on a frictionless road. If the banking angle is 45∘45^\circ, the speed of the car is:

A

20 ms−120 \text{ ms}^{-1}

B

30 ms−130 \text{ ms}^{-1}

C

5 ms−15 \text{ ms}^{-1}

D

10 ms−110 \text{ ms}^{-1}

Step-by-Step Solution

  1. Concept: On a frictionless banked road, the horizontal component of the normal force provides the necessary centripetal force required for circular motion. The optimum speed v0v_0 (where no friction is required) depends only on the radius RR, gravity gg, and banking angle θ\theta [NCERT Physics Class 11, Laws of Motion, Section 4.10, Eq 4.22].
  2. Formula: v=Rgtan⁡θv = \sqrt{Rg \tan\theta}
  3. Given Data:
  • Radius, R=90 mR = 90 \text{ m}
  • Banking angle, θ=45∘\theta = 45^\circ
  • Acceleration due to gravity, g≈10 m/s2g \approx 10 \text{ m/s}^2 (standard approximation for integer answers).
  • Mass m=1000 kgm = 1000 \text{ kg} (Note: Mass cancels out in the derivation and is not needed for the calculation).
  1. Calculation: Substituting the values into the formula: v=90×10×tan⁡(45∘)v = \sqrt{90 \times 10 \times \tan(45^\circ)} Since tan⁡(45∘)=1\tan(45^\circ) = 1: v=900×1v = \sqrt{900 \times 1} v=30 m/sv = 30 \text{ m/s}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from LAWS OF MOTION. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSLAWS OF MOTIONnegotiatesbankedradiusfrictionlessbanking

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