he ratio of S.I unit of angular momentum to linear momentum is:a) J.Sb) N/Jc) J.Nd) J/N​

To solve the problem, we need to understand the S.I. units of angular momentum and linear momentum and then find the ratio between them.

1. Break Down the Problem

• Identify the S.I. unit of angular momentum.
• Identify the S.I. unit of linear momentum.
• Calculate the ratio of these two units.

2. Relevant Concepts

• The S.I. unit of angular momentum $L$ is given by: $L = I \cdot \omega$ where $I$ is the moment of inertia (in kg·m²) and $\omega$ (angular velocity) is in rad/s. Thus, the unit of angular momentum is: $\text{Unit of } L = \text{kg} \cdot \text{m}^2/\text{s}$

• The S.I. unit of linear momentum $p$ is: $p = m \cdot v$ where $m$ is mass (in kg) and $v$ is velocity (in m/s). Thus, the unit of linear momentum is: $\text{Unit of } p = \text{kg} \cdot \text{m/s}$

3. Analysis and Detail

• Now, we calculate the ratio of angular momentum to linear momentum: $\text{Ratio} = \frac{\text{Unit of } L}{\text{Unit of } p} = \frac{\text{kg} \cdot \text{m}^2/\text{s}}{\text{kg} \cdot \text{m/s}}$
• Simplifying this ratio: $= \frac{\text{kg} \cdot \text{m}^2/\text{s}}{\text{kg} \cdot \text{m/s}} = \frac{\text{m}^2}{\text{m}} = \text{m}$

4. Verify and Summarize

• The calculated ratio gives a dimension of meters (m). We need to express this unit in the context of the provided options.

Final Answer

None of the given options (a) J.S, (b) N/J, (c) J.N, or (d) J/N correctly represent the ratio, since the ratio simplifies to meters (m). Therefore, correct answer is not listed among the options.