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Match the column : {:(,"Column-I (Quan...

Match the column :
`{:(,"Column-I (Quantity)",,"Column-II(Unit)"),((a),"Energy density (Energy per unit volume)",(p),"dyne"//cm^(2)),((b),"Force constant of a spring",(r),kg-m//s),((c),"Pressure",(r),erg//cm^(2)),(,,(s),"pascal"):}`

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The correct Answer is:
To solve the problem of matching the quantities in Column-I with their respective units in Column-II, we will analyze each quantity step by step. ### Step 1: Analyze Energy Density - **Quantity**: Energy density (Energy per unit volume) - **Formula**: Energy density = Energy / Volume - **Unit of Energy**: In SI, energy is measured in Joules (J), which is equivalent to kg·m²/s². - **Unit of Volume**: Volume is measured in cubic meters (m³). - **Unit of Energy Density**: \[ \text{Energy Density} = \frac{\text{Energy}}{\text{Volume}} = \frac{\text{kg·m²/s²}}{\text{m³}} = \frac{\text{kg}}{\text{m·s²}} \] - **Matching Unit**: The unit for energy density is not directly given in Column-II, but it can be compared to the options. The closest match in CGS would be erg/cm³, which is equivalent to dyne/cm². ### Step 2: Analyze Force Constant of a Spring - **Quantity**: Force constant of a spring - **Formula**: The force constant (k) is derived from Hooke's Law: F = -kx, where F is force and x is displacement. - **Unit of Force**: In SI, force is measured in Newtons (N), which is kg·m/s². - **Unit of k**: \[ k = \frac{F}{x} = \frac{\text{N}}{\text{m}} = \frac{\text{kg·m/s²}}{\text{m}} = \frac{\text{kg}}{\text{s²}} \] - **Matching Unit**: This matches with the unit given in Column-II as kg·m/s. ### Step 3: Analyze Pressure - **Quantity**: Pressure - **Definition**: Pressure is defined as force per unit area. - **Unit of Pressure**: In SI, pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m². - **Matching Unit**: The unit of pressure is directly given as Pascal (Pa) in Column-II. ### Summary of Matches - **a)** Energy density matches with **(p)** dyne/cm² (as erg/cm³). - **b)** Force constant of a spring matches with **(r)** kg·m/s. - **c)** Pressure matches with **(s)** Pascal. ### Final Matches - **(a)** → (p) - **(b)** → (r) - **(c)** → (s)
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