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JEE Main 2021 (25 Jul, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2021 (25 Jul, Shift 2)

Q40JEE Main 2021 · 25 JUL · SHIFT 2Easy

Applications of Dimensional Analysis

The force is given in terms of time t and displacement x by the equation

F = A cos Bx + C sin Dt

The dimensional formula of ADB\frac{AD}{B} is:

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Answer: (b)

  1. Cosine and sine are dimensionless, so [A]=[F]=[MLT−2][A] = [F] = [MLT^{-2}].
  2. [B]=[L−1][B] = [L^{-1}], [D]=[T−1][D] = [T^{-1}].
  3. [AD/B]=[MLT−2][T−1][L]=[ML2T−3][AD/B] = [MLT^{-2}][T^{-1}][L] = [ML^2T^{-3}].
  4. So the answer is (b).
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