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NEET 2024
Exam
NEET
Year
2024
Subject
Physics
Chapter
Units and Dimensions

NEET 2024 · Physics · Units and Dimensions

A force defined by F=α t^2+β t acts on a particle at a given time t...

A force defined by F=αt2+βtF=\alpha t^2+\beta t acts on a particle at a given time tt. The factor which is dimensionless, if α\alpha and β\beta are constants, is:

Options

  1. Aαt/β\alpha t / \beta
  2. Bαβt\alpha \beta t
  3. Cαβ/t\alpha \beta / t
  4. Dβt/α\beta t / \alpha

Correct answer

A. αt/β\alpha t / \beta

Step-by-step solution

From principle of homogeneity [F]=[αt2]=[βt][α]=[F][t2] and  [β]=[F][t]∴[α][t]=[β]∴αtβ= dimensionless \begin{aligned} & {[F]=\left[\alpha t^2\right]=[\beta t]} \\ & {[\alpha]=\frac{[F]}{\left[t^2\right]} \text{\text{ and } }[\beta]=\frac{[F]}{[t]}} \\ & \therefore \quad[\alpha][t]=[\beta] \\ & \therefore \quad \frac{\alpha t}{\beta}=\text{ dimensionless } \end{aligned}
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