Question

A force defined by F = αt2 + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is :

• A. $\frac{\beta t}{\alpha}$
• B. $\frac{\alpha t}{\beta}$
• C. αβt
• D. $\frac{\alpha\beta}{t}$

Answer 1

Answer: (B)

$\frac{\alpha t}{\beta}$

Answer 2

For $\frac{\alpha t}{\beta}$ to be dimensionless:
- Dimensions of $\alpha$: $[F] \cdot [t]^{-2} = \frac{MLT^{-2}}{T^2} = MLT^{-4}$.
- Dimensions of $\beta$: $[F] \cdot [t]^{-1} = \frac{MLT^{-2}}{T} = MLT^{-3}$.
- $\frac{\alpha t}{\beta}$ is dimensionless since $\frac{MLT^{-4} \cdot T}{MLT^{-3}} = 1$.