Force F is given in terms of time t and displacement x by equation F = A,cos,Bx + C,sin,Dt. dimensio

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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

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