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1.Units, Dimensions and Measurement
easy
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.
Option A
Option B
Option C
Option D
Solution
Now, $[\mathrm{LHS}]=[\mathrm{RHS}]$
$[y]=[\mathrm{A}]=\mathrm{L}$
because $\omega t-k x$ is dimensionless,
$[k x]=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\therefore[\omega t]=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$
$\therefore [k] \mathrm{L}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$
$\therefore[\omega] \mathrm{T}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$
$\therefore [k]=\mathrm{L}^{-1}\therefore[\omega]=\mathrm{T}^{-1}$
Standard 11
Physics
