Assertion : A force of `1kg` f produces an acceleration of `1m//s^(2)` in a body of mass `1kg`
Reason : It follows from a `= f//m` .

Options

A. If both, Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. If both, Assertion and Reason are true but Reason is not a correct explanation of the Assertion
C. If Assertion is ture but the Reason is false
D. If both, Assertion and Reason are false

Explanation

To solve the given problem, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that a force of `1 kgf` produces an acceleration of `1 m/s²` in a body of mass `1 kg`.

### Step 2: Convert the Force
We know that `1 kgf` (kilogram-force) is equivalent to `9.8 N` or approximately `10 N`. For simplicity, we will use `10 N` in our calculations.

### Step 3: Apply Newton's Second Law
According to Newton's second law of motion, the relationship between force (F), mass (m), and acceleration (a) is given by the formula:
\[ F = m \cdot a \]
From this, we can rearrange the formula to find acceleration:
\[ a = \frac{F}{m} \]

### Step 4: Substitute the Values
Now, substituting the values into the equation:
- Force \( F = 10 N \)
- Mass \( m = 1 kg \)

We get:
\[ a = \frac{10 N}{1 kg} = 10 m/s² \]

### Step 5: Compare with the Assertion
The assertion claims that the acceleration is `1 m/s²`, but our calculation shows that the acceleration is `10 m/s²`. Therefore, the assertion is incorrect.

### Step 6: Analyze the Reason
The reason states that the relationship follows from \( a = \frac{F}{m} \). This statement is indeed correct as it is a fundamental principle of Newton's second law.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the final conclusion is that the assertion is incorrect while the reason is correct.

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