Match the items in column I to the items in column II given below `{:(,"Column-I",,"Column-II"),((A),"Planet moving around the sun in the elliptical orbit",(p),"Linear momentum is conserved/constant"),((B),"Planet moving around the sun in the fixed circular orbit",(q),"Angular momentum is conserved about one point in space."),((C ),"A particle of mass " m_(1) " is projected towards a stationary mass " m_(2)." For " m_(1) " and " m_(2) " as system",(r ),"Kinetic energy is conserved"),((D),"A particle of mass m is projected by making an angle " theta " from the surface of the earth with speed less than escape velocity",(s),"Total energy is conserved"):}`

Answer

To match the items in Column I with those in Column II, we analyze each statement in Column I and determine the corresponding conservation laws or principles from Column II.

### Step-by-Step Solution:

1. **For Item A**: "Planet moving around the sun in the elliptical orbit."
- In an elliptical orbit, the only force acting on the planet is the gravitational force from the sun, which is an internal force. Therefore:
- **Total Energy is conserved** (s).
- **Angular Momentum is conserved** about the sun (q).
- **Linear Momentum is not conserved** because the direction of the velocity changes, although the total momentum of the system remains constant.
- **Kinetic Energy is not conserved** in the strict sense because it varies at different points in the orbit.
- **Matches**: (A) → (s), (q).

2. **For Item B**: "Planet moving around the sun in the fixed circular orbit."
- In a circular orbit, the gravitational force provides the necessary centripetal force, and:
- **Total Energy is conserved** (s).
- **Angular Momentum is conserved** (q).
- **Linear Momentum is conserved** in magnitude but not direction.
- **Kinetic Energy is conserved** because the speed is constant.
- **Matches**: (B) → (s), (q), (r).

3. **For Item C**: "A particle of mass m1 is projected towards a stationary mass m2."
- In this case, since there are no external forces acting on the system of m1 and m2:
- **Total Energy is conserved** (s).
- **Linear Momentum is conserved** (p).
- **Angular Momentum is conserved** (q).
- **Kinetic Energy is not conserved** because some kinetic energy may be converted into other forms during the interaction (like heat or deformation).
- **Matches**: (C) → (s), (p), (q).

4. **For Item D**: "A particle of mass m is projected by making an angle theta from the surface of the earth with speed less than escape velocity."
- This is a projectile motion scenario:
- **Total Energy is conserved** (s).
- **Linear Momentum is not conserved** due to the gravitational force acting on the particle.
- **Angular Momentum is conserved** about the point of projection (q).
- **Kinetic Energy is not conserved** in the strict sense because it converts to potential energy at the peak.
- **Matches**: (D) → (s), (q).

### Final Matches:
- (A) → (s), (q)
- (B) → (s), (q), (r)
- (C) → (s), (p), (q)
- (D) → (s), (q)