Question

The velocity v of a particle at time t is given by v = at + $\bigg(\frac{b}{t}+c\bigg)$, where a, b and c are constants, The dimensions of a, b and c are respectively : constants, The dimensions of a, b and c are respectively :

• A. [LT-2 ], [L] and [T]
• B. [L], [T] and [LT2 ]
• C. [L2T2 ], [LT] and [L]
• D. [L], [LT] and [T2]

Answer 1

Answer: (A)

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

Answer 2

Dimensions of Constants: The dimensions of physical quantities can be determined using the equations they appear in.
In the equation v = at + $\bigg(\frac{b}{t}+c\bigg)$, we have:
[v] = [LT-1]
[a] = [LT-2]
[b] = [LT-1T] = [L]
[c] = [t] = [T]
So, the dimensions are: [LT-1] [L] [T] for a, b, and c, respectively.

Therefore, the correct option is (A): [LT-2 ], [L] and [T]