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NEET PHYSICSLAWS OF MOTIONMedium

Question

A block of mass mm is placed on a smooth inclined wedge ABC of inclination θ\theta as shown in the figure. The wedge is given an acceleration 'aa' towards the right. The relation between aa and θ\theta for the block to remain stationary on the wedge is:

A

a=gcsc⁡θa = g \csc \theta

B

a=gsin⁡θa = g \sin \theta

C

a=gcos⁡θa = g \cos \theta

D

a=gtan⁡θa = g \tan \theta

Step-by-Step Solution

  1. Frame of Reference: Analyze the problem from the non-inertial frame of reference of the wedge, which is accelerating with acceleration aa towards the right.
  2. Pseudo Force: In this non-inertial frame, a pseudo force of magnitude mama acts on the block of mass mm. Since the wedge accelerates to the right, the pseudo force acts to the left.
  3. Forces on the Block:
  • Weight (mgmg) acting vertically downwards.
  • Normal Reaction (NN) acting perpendicular to the incline.
  • Pseudo Force (mama) acting horizontally towards the left.
  1. Equilibrium Condition: For the block to remain stationary relative to the wedge, the net force along the incline must be zero.
  • Component of weight down the incline: mgsin⁡θmg \sin \theta.
  • Component of pseudo force up the incline: macos⁡θma \cos \theta.
  1. Calculation: Equating the components along the incline: macos⁡θ=mgsin⁡θma \cos \theta = mg \sin \theta a=gsin⁡θcos⁡θa = g \frac{\sin \theta}{\cos \theta} a=gtan⁡θa = g \tan \theta (Reference: NCERT Class 11, Physics Part I, Chapter 5, Laws of Motion).

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 MOTIONplacedsmoothinclinedinclinationfigure

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