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1.Units, Dimensions and Measurement
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The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
A
${M^0}{L^0}{T^0}$
B
${M^0}{L^0}{T^{ - 1}}$
C
${M^0}{L^{ - 1}}{T^0}$
D
${M^0}{L^1}{T^{ - 1}}$
Solution
$F=A \cos B x+C \sin D t$
the argument, $\theta$ of cos or sin should be dimensionless.
therefore,
dimension of $\mathrm{Bx}=[M L T]$
$[B]\left[L^{\prime}\right]=[M L T]$
$[B]=\left[M L^{0} T\right]$
Similarly $[D]\left[T^{\prime}\right]=[M L T]$
$[D]=\left[M L T^{0}\right.$
dimension of $D/B=\frac{\left[M L T^{0}\right]}{\left[M L^{0} T\right]}$
$=\left[L^{1} T^{-1}\right]$
Standard 11
Physics
