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NEET 1990 (AIPMT) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from NEET 1990 (AIPMT)

Q83NEET 1990 · AIPMTEasy

Applications of Dimensional Analysis

The frequency of vibration ff of a mass mm suspended from a spring of spring constant kk is given by a relation f=amxkyf = am^xk^y, where aa is a dimensionless constant. The values of xx and yy are

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Answer: (d)

  1. [f]=T−1[f] = T^{-1}, [m]=M[m] = M, [k]=MT−2[k] = MT^{-2}.
  2. T−1=Mx+yT−2yT^{-1} = M^{x+y}T^{-2y}, so x+y=0x + y = 0 and −2y=−1-2y = -1.
  3. y=12y = \frac{1}{2}, x=−12x = -\frac{1}{2} (so f∝k/mf \propto \sqrt{k/m}).
  4. So the answer is (d).
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