Question

If the force is given by \( F = at + bt^2 \) with \( t \) as time, then the dimensions of \( a \) and \( b \) are:

• A. [MLT\(^-4\)] and [MLT\(^-3\)]
• B. [MLT\(^-3\)] and [MLT\(^-4\)]
• C. [MLT\(^-3\)] and [MLT\(^-2\)]
• D. [MLT\(^-2\)] and [MLT\(^-3\)]

Hint:

Use dimension analysis to check the consistency of physical equations.

Answer 1

The Correct Option is B

Step 1: Dimension analysis.
The force is given by: \[ F = at + bt^2 \] The dimensions of force \( F \) are [MLT\(^-2\)].

Step 2: Dimension of \( a \).
For the term \( at \) to have dimensions of force, the dimension of \( a \) must be [MLT\(^-3\)].

Step 3: Dimension of \( b \).
For the term \( bt^2 \) to have dimensions of force, the dimension of \( b \) must be [MLT\(^-4\)]. Thus, the correct answer is (2).