JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The force is given in terms of time \(t\) and displacement \(x\) by the equation \({F}={A} \cos {Bx}+{C} \sin {Dt}\) The dimensional formula of \(\frac{{AD}}{{B}}\) is -
- A \(\left[{ML}^{2} {T}^{-3}\right]\)
- B \(\left[{M}^{2} L^{2} {T}^{-3}\right]\)
- C \(\left[{M}^{1} {L}^{1} {T}^{-2}\right]\)
- D \(\left[{M}^{0} {LT}^{-1}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[{ML}^{2} {T}^{-3}\right]\)
Step-by-step Solution
Detailed explanation
\(\theta\) of cos or sin should be dimensionless. \({[ A ]=\left[ MLT ^{-2}\right] }\) \({[ B ]=\left[ L ^{-1}\right] }\) \({[ D ]=\left[ T ^{-1}\right] }\) \({\left[\frac{ AD }{ B }\right]=\frac{\left[ MLT ^{-2}\right]\left[ T ^{-1}\right]}{\left[ L ^{-1}\right]} }\)…
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