Question

The velocity v of a particle depends upon the time t according to the equation $v=a+bt+\frac{c}{d+t}$ = The dimensions of a, b, c and d are

• A. [LT^-1], [LT^-2], [L], [T]
• B. [L], [T], [LT^-1], [LT^-2]
• C. [LT^-2], [L], [T], [LT^-1]
• D. [T], [L], [LT^-1], [LT^-2]

Answer 1

The correct option is A

[LT^-1], [LT^-2], [L], [T]

From principle of homogeneity [a]=[v]

$Or\left[a\right]=\left[L{T}^{-1}\right]\left[bt\right]=\left[v\right]Or\left[bT\right]=\left[L{T}^{-1}\right]Or\left[b\right]=\left[L{T}^{-2}\right]\left[b\right]\left[t\right]Or\left[d\right]=\left[T\right]\left[\frac{c}{d+t}\right]=\left[v\right]\left[c\right]=\left[v\right][d+t]=\left[L{T}^{-1}\right]\left[T\right]\left[c\right]=\left[L\right]$