Statement-1: Kepler's law of areas is equivalent to the law of conservation of angular momentum
Statement-2: Areal velocity `(dA)/(dt)=(L)/(2m)=` constant

Options

A. Statement-1 is true, statement-2 is true: Statement-2 is a correct explanation for statement-1
B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1
C. Statement-1 is true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.

Answer

To solve the problem, we need to analyze both statements given in the question and determine their validity and relationship.

### Step 1: Understand Kepler's Law of Areas
Kepler's law of areas states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that the areal velocity (the rate at which area is swept out) is constant.

**Hint for Step 1:** Recall the definition of Kepler's law of areas and its implications on the motion of planets.

### Step 2: Define Areal Velocity
Areal velocity can be mathematically expressed as:
\[ \frac{dA}{dt} = \frac{L}{2m} \]
where \(dA\) is the area swept out in a time interval \(dt\), \(L\) is the angular momentum, and \(m\) is the mass of the planet.

**Hint for Step 2:** Remember that areal velocity relates to the angular momentum of the planet and its mass.

### Step 3: Conservation of Angular Momentum
In a closed system where no external torques act, the angular momentum \(L\) of an object remains constant. This conservation leads to the conclusion that the areal velocity, which is dependent on \(L\), is also constant.

**Hint for Step 3:** Think about the implications of conservation laws in physics, particularly how they relate to motion.

### Step 4: Analyze Statement 1
Statement 1 claims that Kepler's law of areas is equivalent to the law of conservation of angular momentum. Since the areal velocity is constant due to the conservation of angular momentum, this statement is indeed true.

**Hint for Step 4:** Consider how the constancy of areal velocity reflects the conservation of angular momentum.

### Step 5: Analyze Statement 2
Statement 2 states that the areal velocity \(\frac{dA}{dt} = \frac{L}{2m}\) is constant. Since we established that angular momentum is conserved, this statement is also true.

**Hint for Step 5:** Verify the relationship between areal velocity and angular momentum to confirm the truth of this statement.

### Step 6: Conclusion
Both statements are true, and Statement 2 provides the correct explanation for Statement 1. Therefore, the answer is that both statements are correct, and Statement 2 explains Statement 1.

**Final Answer:** Both statements are true, and Statement 2 is the correct explanation of Statement 1.