A force `F=(3hati+2hatj+6hatk)N` produces acceleration of `1m//s^2` in a body. The mass of the body is

Options

A. `4sqrt2kg`
B. 7 kg
C. `7sqrt2kg`
D. `5sqrt2kg`

Answer

To solve the problem, we need to find the mass of the body using the given force and acceleration. We can use Newton's second law of motion, which states that:

\[ F = m \cdot a \]

Where:
- \( F \) is the force acting on the body,
- \( m \) is the mass of the body,
- \( a \) is the acceleration of the body.

### Step-by-step Solution:

1. **Identify the given values:**
- The force \( F \) is given as \( F = (3\hat{i} + 2\hat{j} + 6\hat{k}) \, \text{N} \).
- The acceleration \( a \) is given as \( 1 \, \text{m/s}^2 \).

2. **Convert the force from vector form to scalar form:**
- To find the magnitude of the force, we use the formula for the magnitude of a vector:
\[ |F| = \sqrt{(3^2 + 2^2 + 6^2)} \]
- Calculate the squares:
\[ 3^2 = 9, \quad 2^2 = 4, \quad 6^2 = 36 \]
- Sum these values:
\[ 9 + 4 + 36 = 49 \]
- Take the square root:
\[ |F| = \sqrt{49} = 7 \, \text{N} \]

3. **Use Newton's second law to find the mass:**
- We know from Newton's second law that:
\[ F = m \cdot a \]
- Substitute the values we have:
\[ 7 = m \cdot 1 \]
- Solve for mass \( m \):
\[ m = 7 \, \text{kg} \]

### Final Answer:
The mass of the body is \( 7 \, \text{kg} \).

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