In the relation $x = \cos \left( {{\rm{\omega }}t + kx} \right),$ the dimensions of ω are

$\left[ {{{\rm{M}}^0}{{\rm{L}}^0}{{\rm{T}}^{ - 1}}} \right]$

$\left[ {{{\rm{M}}^0}{\rm{LT}}} \right]$

$\left[ {{{\rm{M}}^0}{{\rm{L}}^{ - 1}}{{\rm{T}}^0}} \right]$

$\left[ {{{\rm{M}}^0}{\rm{L}}{{\rm{T}}^{ - 1}}} \right]$

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NEET UG PHYSICS MCQ: UNITS & MEASUREMENTS

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Application +4 | -1

In the relation

x = \cos \left( {\mathrm{\omega }t + kx} \right),

the dimensions of ω are

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Correct option: C

\left[ {{\mathrm{M}^0}{\mathrm{L}^0}{\mathrm{T}^{ - 1}}} \right]

Option C

\left[ {{\mathrm{M}^0}{\mathrm{L}^0}{\mathrm{T}^{ - 1}}} \right]

is correct because the argument of a trigonometric function must be dimensionless, so ωt must be dimensionless, making ω have dimensions of inverse time.

NEET UG PHYSICS MCQ: UNITS & MEASUREMENTS

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