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PhysicsNEET 2024SI units, dimensions and dimensional analysis

Units and Measurements

A force defined by F=αt2+βtF = \alpha t^2 + \beta t acts on a particle at a given time tt. The factor which is dimensionless, if α\alpha and β\beta are constants, is:

  1. A.αtβ\dfrac{\alpha t}{\beta}✓
  2. B.αt\alpha t
  3. C.βt\beta t
  4. D.βtα\dfrac{\beta t}{\alpha}

Solution

αt2\alpha t^2 and βt\beta t both have the dimensions of force, so [αt]=[β][\alpha t] = [\beta]. Hence αtβ\frac{\alpha t}{\beta} is dimensionless.

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