AP EAMCET · PHYSICS · Units and Dimensions
If the equation for the velocity of a particle at time ' \(t\) ' is \(v=a t+\frac{b}{t+c}\), then the dimensions of \(a, b, c\) are respectively
- A \(\mathrm{LT}^{-2}, \mathrm{~L}, \mathrm{~T}\)
- B \(\mathrm{L}^2, \mathrm{~L}, \mathrm{~T}\)
- C \(\mathrm{LT}^{-2}, \mathrm{LT}, \mathrm{L}\)
- D \(\mathrm{L}, \mathrm{LT}, \mathrm{L}^2\)
Answer & Solution
Correct Answer
(A) \(\mathrm{LT}^{-2}, \mathrm{~L}, \mathrm{~T}\)
Step-by-step Solution
Detailed explanation
Dimension of \(c\): Since \(t\) and \(c\) are added, \( [c] = [t] = \mathrm{T} \) Dimension of \(a\): From \(v=at\), \( [a][t] = [v] \Rightarrow [a]\mathrm{T} = \mathrm{LT}^{-1} \Rightarrow [a] = \mathrm{LT}^{-2} \) Dimension of \(b\): From \(v=\frac{b}{t+c}\),…
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