STATEMENT -1 : If a body is projected from a satellite so as to escape then its velocity of projection with respect to the satellite depends upon the direction of projection.
STATEMENT -2 : Speed of a planet revolving around the sun in an elliptical orbit is maximum at perigee and minimum at apogee.
STATEMENT - 3 : Gravitational field is conservative in nature.

Options

A. F F F
B. T T F
C. T F F
D. F T T

Answer

To analyze the statements provided in the question, we will evaluate each statement one by one and determine their validity.

### Step 1: Evaluate Statement 1
**Statement 1:** If a body is projected from a satellite so as to escape, then its velocity of projection with respect to the satellite depends upon the direction of projection.

**Analysis:**
- The escape velocity from a satellite is the minimum velocity required for an object to break free from the gravitational pull of the satellite without any additional propulsion.
- The escape velocity is given by the formula:
\[ v_{escape} = \sqrt{\frac{2GM}{R}} \]
where \(G\) is the gravitational constant, \(M\) is the mass of the satellite, and \(R\) is the distance from the center of the satellite to the object.
- The escape velocity is a scalar quantity and does not depend on the direction of projection; it only depends on the mass of the satellite and the distance from its center.
- Therefore, **Statement 1 is false.**

### Step 2: Evaluate Statement 2
**Statement 2:** Speed of a planet revolving around the sun in an elliptical orbit is maximum at perigee and minimum at apogee.

**Analysis:**
- According to Kepler's laws of planetary motion, a planet moves faster when it is closer to the sun (at perigee) and slower when it is farther from the sun (at apogee).
- The conservation of angular momentum states that the angular momentum \(L\) is constant:
\[ L = mvr \]
where \(m\) is mass, \(v\) is velocity, and \(r\) is the distance from the sun.
- As \(r\) decreases (at perigee), \(v\) must increase to keep \(L\) constant. Conversely, as \(r\) increases (at apogee), \(v\) must decrease.
- Therefore, **Statement 2 is true.**

### Step 3: Evaluate Statement 3
**Statement 3:** Gravitational field is conservative in nature.

**Analysis:**
- A conservative field is one in which the work done by the field on an object moving from one point to another is independent of the path taken.
- The gravitational field is indeed conservative because the work done by gravity only depends on the initial and final positions, not the path taken.
- This means that gravitational potential energy can be defined, and energy is conserved in gravitational interactions.
- Therefore, **Statement 3 is true.**

### Conclusion
- **Statement 1:** False
- **Statement 2:** True
- **Statement 3:** True

The correct option based on the evaluation is **Option B** (False, True, True).

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