The physical quantity in translational motion, which is analogous to moment of inertia in rotational motion is

Options

A. mass
B. distance
C. time
D. speed

Answer

To solve the question, we need to find the physical quantity in translational motion that is analogous to the moment of inertia in rotational motion.

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
- Moment of inertia (I) is a measure of an object's resistance to changes in its rotation. It depends on the mass of the object and how that mass is distributed relative to the axis of rotation.

2. **Kinetic Energy Comparison**:
- The kinetic energy in translational motion is given by the formula:
\[ KE_{trans} = \frac{1}{2} mv^2 \]
- The kinetic energy in rotational motion is given by:
\[ KE_{rot} = \frac{1}{2} I \omega^2 \]
- Here, \(m\) is mass, \(v\) is linear velocity, \(I\) is moment of inertia, and \(\omega\) is angular velocity.

3. **Momentum Comparison**:
- The linear momentum (p) in translational motion is given by:
\[ p = mv \]
- The angular momentum (L) in rotational motion is given by:
\[ L = I \omega \]

4. **Identifying Analogous Quantities**:
- In translational motion, mass (m) is a key quantity that determines how much inertia an object has when it is moving in a straight line.
- In rotational motion, moment of inertia (I) serves a similar purpose for rotational motion, determining how much inertia an object has when it is rotating.

5. **Conclusion**:
- Since mass (m) in translational motion is analogous to moment of inertia (I) in rotational motion, we conclude that the answer to the question is:
\[ \text{Mass} \]

### Final Answer:
The physical quantity in translational motion that is analogous to moment of inertia in rotational motion is **Mass**.

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