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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
The velocity $v$ (in $cm/\sec $) of a particle is given in terms of time $t$ (in sec) by the relation $v = at + \frac{b}{{t + c}}$ ; the dimensions of $a,\,b$ and $c$ are
  • A
    $a = {L^2},\,b = T,\,c = L{T^2}$
  • B
    $a = L{T^2},\,b = LT,\,c = L$
  • ✓
    $a = L{T^{ - 2}},b = L,\,c = T$
  • D
    $a = L,\,b = LT,\,c = {T^2}$
✓

Answer

Correct option: C.
$a = L{T^{ - 2}},b = L,\,c = T$
c
(c) From the principle of dimensional homogenity $[v] = [at] \Rightarrow [a] = [L{T^{ - 2}}]$.

Similarly $[b] = [L]{\rm{ and}}\;[c] = [T]$

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