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

The Correct Option is A

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]