Assertion : Range of projectile of projection of a body is made n times . Its time of fights becomes n times .
Reason Range of jprojectile does not depend on the initial velocity of a body .

Options

A. If both assertion and reason are ture and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reson are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understanding the Assertion
The assertion states that if the range of a projectile is made n times, then its time of flight also becomes n times.

- **Formula for Range (R)**:
\[ R = \frac{u^2 \sin 2\theta}{g} \]

- **Formula for Time of Flight (T)**:
\[ T = \frac{2u \sin \theta}{g} \]

### Step 2: Analyzing the Change in Range
If the range is increased by n times, we can express this as:
\[ R' = nR = n \left(\frac{u^2 \sin 2\theta}{g}\right) \]

### Step 3: Finding New Initial Velocity
Let the new initial velocity be \( u' \). Then we can write:
\[ R' = \frac{(u')^2 \sin 2\theta}{g} \]
Setting the two expressions for \( R' \) equal gives:
\[ n \left(\frac{u^2 \sin 2\theta}{g}\right) = \frac{(u')^2 \sin 2\theta}{g} \]
This simplifies to:
\[ n u^2 = (u')^2 \]
Taking the square root of both sides, we find:
\[ u' = \sqrt{n} u \]

### Step 4: Finding New Time of Flight
Now, we can find the new time of flight \( T' \) using the new initial velocity \( u' \):
\[ T' = \frac{2u' \sin \theta}{g} = \frac{2(\sqrt{n} u) \sin \theta}{g} = \sqrt{n} \left(\frac{2u \sin \theta}{g}\right) = \sqrt{n} T \]

### Step 5: Conclusion
From the calculations, we see that:
- The time of flight \( T' \) becomes \( \sqrt{n} T \), not \( n T \). Therefore, the assertion is incorrect.

### Step 6: Analyzing the Reason
The reason states that the range of a projectile does not depend on the initial velocity of a body. However, from the formula for range, we see that it does depend on the initial velocity \( u \). Therefore, the reason is also incorrect.

### Final Answer
Both the assertion and the reason are false.