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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Physics
Chapter
Units and Dimensions

BITSAT 2021 · Physics · Units and Dimensions

If force (F) , length (L) and time (T) are assumed to be...

If force (F)(F), length (L)(L) and time (T)(T) are assumed to be fundamental units, then the dimensional formula of the mass will be

Options

  1. A[FL−1 T2]\left[\mathrm{FL}^{-1} \mathrm{~T}^{2}\right]
  2. B[FL−1 T−2]\left[\mathrm{FL}^{-1} \mathrm{~T}^{-2}\right]
  3. C[FL−1 T−1]\left[\mathrm{FL}^{-1} \mathrm{~T}^{-1}\right]
  4. D[FL2 T2]\left[\mathrm{FL}^{2} \mathrm{~T}^{2}\right]

Correct answer

D. [FL2 T2]\left[\mathrm{FL}^{2} \mathrm{~T}^{2}\right]

Step-by-step solution

Let m=KFaLbTc\mathrm{m}=\mathrm{KF}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}} Substituting the dimensions of [F]=[MLT−2],[L]=[L][\mathrm{F}]=\left[\mathrm{MLT}^{-2}\right],[\mathrm{L}]=[\mathrm{L}] and [T]=[T][\mathrm{T}]=[\mathrm{T}] and comparing both side, we get m=FL−1T2\mathrm{m}=\mathrm{FL}^{-1} \mathrm{ T}^{2}
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