Match the following
`{: ( "Column I", " Column II"),( "(A)Work", " (p)Slope of (momentum- time)P-t graph") , ("(B) Power " , "(q) Slope of W - t graph"),(" (C)Force" , "(r) Area under F-s graph") , ( "(D)Impulse" , " (iv) Area under F- t graph"):}`

Options

A. A -q, B - p, C -s, D - r
B. A-r, B-q,C-p, D-s
C. A-s, B-q,C-p, D-r
D. A-q, B-r,C-s, D-p

Explanation

To solve the matching question, we need to analyze each term in Column I and find its corresponding term in Column II based on the definitions and relationships in physics.

### Step-by-Step Solution:

1. **Work (A)**:
- Work done is defined as the integral of force over displacement. Mathematically, it can be expressed as:
\[ W = \int \mathbf{F} \cdot d\mathbf{s} \]
- The work done by a force can also be represented as the area under the Force vs. Displacement graph. Therefore, we can match:
\[ (A) \text{ Work } \rightarrow (r) \text{ Area under F-s graph} \]

2. **Power (B)**:
- Power is defined as the rate of doing work. It can be expressed as:
\[ P = \frac{dW}{dt} \]
- The slope of the Work vs. Time graph gives us power. Hence, we can match:
\[ (B) \text{ Power } \rightarrow (q) \text{ Slope of W-t graph} \]

3. **Force (C)**:
- Force is defined as the rate of change of momentum. Mathematically, it can be expressed as:
\[ F = \frac{dp}{dt} \]
- The slope of the Momentum vs. Time graph gives us force. Therefore, we can match:
\[ (C) \text{ Force } \rightarrow (p) \text{ Slope of (momentum-time) P-t graph} \]

4. **Impulse (D)**:
- Impulse is defined as the change in momentum, which can be expressed as:
\[ \text{Impulse} = \Delta p = \int F dt \]
- The area under the Force vs. Time graph gives us impulse. Thus, we can match:
\[ (D) \text{ Impulse } \rightarrow (s) \text{ Area under F-t graph} \]

### Final Matches:
- (A) Work → (r) Area under F-s graph
- (B) Power → (q) Slope of W-t graph
- (C) Force → (p) Slope of (momentum-time) P-t graph
- (D) Impulse → (s) Area under F-t graph

### Summary of Matches:
- A → r
- B → q
- C → p
- D → s