Units and Measurements

The velocity v of a particle at time t is given by v = at + bt+c, where a, b and c are constants. The dimensions of a, b and c are

1. [L], [LT] and [LT-2]
2. [LT-2], [L] and [T]
3. [L2], [T] and [LT-2]
4. [LT-2], [LT] and [L]

Answer

(2) [LT-2], [L] and [T]

Solution

By the principle of homogeneity, every term has the dimensions of velocity [LT-1].

[at] = [LT-1] ⇒ [a] = [LT-1][T] = [LT-2]

c is added to t ⇒ [c] = [T]

[ bt+c ] = [LT-1] ⇒ [b] = [LT-1][T] = [L]

∴ a, b, c: [LT-2], [L] and [T]

Answer: (2)