Assertion `:-` In projectile motion a particle is projected at some angle from horizontal. At highest point of its path radius of curvature is least.
At highest point of path normal acceleration of projectile is equal to acceleration due to gravity.

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Answer

To solve the question, we need to analyze the assertion and the reason provided regarding projectile motion.

### Step 1: Understanding the Assertion
The assertion states that in projectile motion, when a particle is projected at some angle from the horizontal, at the highest point of its path, the radius of curvature is least.

**Hint:** Recall the concept of radius of curvature in the context of projectile motion.

### Step 2: Analyzing the Highest Point
At the highest point of the projectile's trajectory, the vertical component of the velocity becomes zero, and only the horizontal component remains. The projectile is momentarily at rest in the vertical direction.

**Hint:** Consider the components of velocity at the highest point.

### Step 3: Normal Acceleration at the Highest Point
The reason states that at the highest point of the path, the normal acceleration of the projectile is equal to the acceleration due to gravity (g). In projectile motion, the normal acceleration (centripetal acceleration) is given by the formula \( a_n = \frac{V^2}{R} \), where \( V \) is the horizontal velocity and \( R \) is the radius of curvature.

**Hint:** Remember that at the highest point, the vertical velocity is zero, and the only acceleration acting on the projectile is gravity.

### Step 4: Relating Radius of Curvature and Normal Acceleration
At the highest point, we can express the radius of curvature \( R \) as:
\[ R = \frac{V^2}{g} \]
where \( V \) is the horizontal component of velocity at that point. Since \( V \) is at its minimum (the horizontal component remains constant, but the vertical component is zero), the radius of curvature \( R \) will be minimized.

**Hint:** Think about how the values of \( V \) and \( g \) affect the radius of curvature.

### Step 5: Conclusion
Both the assertion and the reason are true. The radius of curvature is indeed least at the highest point of the projectile's path, and the normal acceleration equals the acceleration due to gravity. Therefore, the reason correctly explains the assertion.

**Final Answer:** Both the assertion and reason are true, and the reason is the correct explanation of the assertion.