The quantities which corresponds in linear motion to the quantities I, `vecJ, vectau and vecomega` in rotatory motion are respectively.

Options

A. `M, vecp, vecF and vecv`
B. `m, vecF, vecv and vecp`
C. `M, vecp, vecv and vecF`
D. `eta, vec tau, vecp and vec tau`

Answer

To solve the problem, we need to identify the linear motion quantities that correspond to the given rotational motion quantities: \( I \) (moment of inertia), \( \vec{J} \) (angular momentum), \( \vec{\tau} \) (torque), and \( \vec{\omega} \) (angular velocity).

### Step-by-Step Solution:

1. **Identify the quantity \( I \)**:
- In rotational motion, \( I \) represents the moment of inertia, which is a measure of an object's resistance to changes in its rotational motion. It is analogous to mass in linear motion.
- **Corresponding linear quantity**: Mass (\( m \))

2. **Identify the quantity \( \vec{J} \)**:
- \( \vec{J} \) represents angular momentum in rotational motion. Angular momentum is the rotational equivalent of linear momentum.
- **Corresponding linear quantity**: Linear momentum (\( \vec{p} \))

3. **Identify the quantity \( \vec{\tau} \)**:
- \( \vec{\tau} \) represents torque in rotational motion, which is the rotational equivalent of force in linear motion.
- **Corresponding linear quantity**: Force (\( \vec{F} \))

4. **Identify the quantity \( \vec{\omega} \)**:
- \( \vec{\omega} \) represents angular velocity in rotational motion, which is the rotational equivalent of linear velocity.
- **Corresponding linear quantity**: Linear velocity (\( \vec{v} \))

### Summary of Correspondences:
- \( I \) (moment of inertia) corresponds to \( m \) (mass)
- \( \vec{J} \) (angular momentum) corresponds to \( \vec{p} \) (linear momentum)
- \( \vec{\tau} \) (torque) corresponds to \( \vec{F} \) (force)
- \( \vec{\omega} \) (angular velocity) corresponds to \( \vec{v} \) (linear velocity)

### Final Answer:
The quantities which correspond in linear motion to the quantities \( I, \vec{J}, \vec{\tau}, \) and \( \vec{\omega} \) in rotational motion are respectively:
- \( m, \vec{p}, \vec{F}, \vec{v} \)