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AIIMS 2014
Exam
AIIMS
Year
2014
Subject
Physics
Chapter
Units and Dimensions

AIIMS 2014 · Physics · Units and Dimensions

If the units of length, mass and force are chosen as fundamental...

If the units of length, mass and force are chosen as fundamental units, the dimensions of time would be

Options

  1. A[M1/2 L−1/2 F1/2]\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{-1 / 2} \mathrm{~F}^{1 / 2}\right]
  2. B[M1/2 L1/2 F1/2]\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{1 / 2}\right]
  3. C[M1/2 L1/2 F−1/2]\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{-1 / 2}\right]
  4. D[M1/2 L−1/2 F−1/2]\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{-1 / 2} \mathrm{~F}^{-1 / 2}\right]

Correct answer

C. [M1/2 L1/2 F−1/2]\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{-1 / 2}\right]

Step-by-step solution

 As F=[MLT−2] or  [T2]=[ML][F] or [T]=[M1/2L1/2F−1/2]\begin{aligned} \text{ As } F=\left[\mathrm{MLT}^{-2}\right] \text{\text{ or } } & {\left[\mathrm{T}^2\right]=\frac{[\mathrm{ML}]}{[\mathrm{F}]} } \\ \text{ or }[\mathrm{T}] & =\left[\mathrm{M}^{1 / 2} \mathrm{ L}^{1 / 2} \mathrm{ F}^{-1 / 2}\right]\end{aligned}
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