Question

The velocity $\upsilon$ (in cm/s) of a particle is given in terms of time (t) by the equation: $\upsilon =at+\frac{b}{t+c}.$ Dimensions of a, b and c are

• A. $A-L^2,B-T,C-L{T}^2$
• B. $A-L{T}^{-2},B-LT,C-L$
• C. $A-L{T}^{-2},B-L,C-T$
• D. $A-L,B-LT,C-T^2$

Answer 1

The correct option is C

$A-L{T}^{-2},B-L,C-T$

$v=at+\frac{b}{t+c}\left[at\right]=\left[v\right]\left[L{T}^{-1}\right]\left[a\right]=\frac{\left[L{T}^{-1}\right]}{T}=\left[L{T}^{-2}\right]\text{Dimensions of}c=\left[c\right]=\left[T\right]\text{(We can add quantities of same dimensions only.)}\left[\frac{b}{t+c}\right]=\left[v\right]=\left[L{T}^{-1}\right]\left[b\right]=\left[L{T}^{-1}\right]\left[T\right]=\left[L\right]$