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Physics · Units, Dimensions & Error Analysis

JEE Main 2024 — 4 April, Shift 1 — Question 42

The equation of stationary wave is : y=2asin⁡(2πntλ)cos⁡(2πxλ)y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right). Which of the following is NOT correct?

  1. Option A:

    The dimensions of nt is [L]

  2. Option B:

    The dimensions of n is [LT−1]\left[\mathrm{LT}^{-1}\right]

  3. Option C:

    The dimensions of n/λn / \lambda is [T]

    Correct
  4. Option D:

    The dimensions of xx is [L]

Answer: C

Step-by-step solution

Comparing the given equation with standard equation of standing wave

2πnλ=ω  &  2πλ=k\frac{2 \pi n}{\lambda}=\omega \; \& \;\frac{2 \pi}{\lambda}=\mathrm{k}

[nλ]=[ω]=T−1\left[\frac{\mathrm{n}}{\lambda}\right]=[\omega]=\mathrm{T}^{-1}

[nt]=[λ]=L[\mathrm{nt}]=[\lambda]=\mathrm{L}

[n]=[λω]=LT−1[\mathrm{n}]=[\lambda \omega]=\mathrm{LT}^{-1}

[x]=[λ]=L[\mathrm{x}]=[\lambda]=\mathrm{L}

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
4 April, Shift 1
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Units and Dimensions Analysis

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