Question

Match List I with List II and select the correct answer.
$\begin{array}{cc}\text{List I(Physical quantity)}& \text{List II (Dimensions)}\\ \text{A. Force}& {\text{1. T}}^{-1}\\ \text{B. Angular velocity}& {\text{2. MLT}}^{-2}\\ \text{C. Torque}& {\text{3. ML}}^{-1}{\text{T}}^{-2}\\ \text{D. Stress}& {\text{4. ML}}^{-1}{\text{T}}^{-1}\\ & {\text{5. ML}}^2{\text{T}}^{-2}\end{array}$

• A. $A\to 5,B\to 4,C\to 3,D\to 1$
• B. $A\to 2,B\to 1,C\to 3,D\to 4$
• C. $A\to 1,B\to 2,C\to 3,D\to 5$
• D. $A\to 2,B\to 1,C\to 5,D\to 3$

Answer 1

The correct option is D $A\to 2,B\to 1,C\to 5,D\to 3$

Dimension of force $=\left[ML{T}^{-2}\right]$

Angular velocity $\omega =\frac{\theta }{t}$ where dimension of plane angle $\theta$ is $\left[M^0{L}^0{T}^0\right]$

$\therefore$ Dimension of angular velocity $=\left[T^{-1}\right]$

Torque = Force $\times$ perpendicular distance $=M{L}^2{\text{T}}^{-2}$

Stress = Force per unit area $=M{L}^{-1}{\text{T}}^{-2}$