If force (F), acceleration (A), Time (T) are used as fundamental units, the dimensional formula for length will be-

This question was previously asked in
UP TGT Science 2011 Official Paper (held on 2016)
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  1. [ F0AT2]
  2. [ FAT2]
  3. [ FA0 T0]
  4. [FAT]

Answer (Detailed Solution Below)

Option 1 : [ F0AT2]
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CONCEPT:

  • Dimensional Formula: The dimensions of a physical quantity represents its nature. 
  • ​Dimensional Formula can help us in finding the relationship between different physical quantities.
    • For example, Dimensional Formula for work done and Kinetic Energy is the same. So, we can say they are related.
  • For dimensionless quantitiesdimensional analysis can't be possible.
    • For example, Relative density is a dimensionless quantity which is the ratio of two densities. we cannot find the dimension of relative density
  • The dimension of fundamental quantities are known and dimensional formulas for other quantities are derived from fundamental units.
  • Example:
    • Finding Dimension of Density:
    1. The expression for density is Mass / Volume
    2. Mass is a fundamental unit with dimension M.
    3. Volume is a cube of length. So, Dimensional Formula for Length L3
    4. Dimensional Formula for density M / L3 = ML -3

EXPLANATION:

From the definition of acceleration,

\(A = \frac{{dv}}{{dt}} = \frac{{{d^2}x}}{{d{t^2}}}\)

\(\smallint dv = \smallint A\;dt\)

V = A × T

\(\frac{x}{T} = A\;T\)

⇒ x = A T2

To write in the form of Dimensions

x = [F0AT2]

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