Question

A force is represented by \( F = ax^2 + b t^{1/2} \) Where \( x = \) distance and \( t = \) time. The dimensions of \( \frac{b^2}{a} \) are:

• A. \( [ML^3T^{-3}] \)
• B. \( [MLT^{-2}] \)
• C. \( [ML^{-1}T^{-1}] \)
• D. \( [ML^2T^3] \)

Answer 1

The Correct Option is A

Given:

\[ F = ax^2 + bt^{1/2} \]

The dimensions of \( a \) are given by:

\[ [a] = \left[ \frac{F}{x^2} \right] = [MLT^{-2}][L]^{-2} = [ML^{-1}T^{-2}] \]

The dimensions of \( b \) are given by:

\[ [b] = \left[ \frac{F}{t^{1/2}} \right] = [MLT^{-2}][T^{-1/2}] = [MLT^{-5/2}] \]

Now, the dimensions of \( \frac{b^2}{a} \) are:

\[ \left[ \frac{b^2}{a} \right] = \frac{[M^2L^2T^{-5}]}{[ML^{-1}T^{-2}]} = [ML^3T^{-3}] \]