A body under the action of a force `vec(F)=6hat(i)-8hat(j)N` acquires an acceleration of `5ms^(-2)` . The mass of the body is

Options

A. 1. 2kg
B. 2. 5kg
C. 3. 4kg
D. 4. 6kg

Explanation

To solve the problem, we need to find the mass of the body given the force acting on it and its acceleration. We can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

### Step-by-Step Solution:

1. **Identify the given values**:
- The force acting on the body is given as \(\vec{F} = 6\hat{i} - 8\hat{j} \, \text{N}\).
- The acceleration of the body is given as \(a = 5 \, \text{m/s}^2\).

2. **Calculate the magnitude of the force**:
- The magnitude of the force \(|\vec{F}|\) can be calculated using the formula:
\[ |\vec{F}| = \sqrt{(F_x)^2 + (F_y)^2} \]
- Here, \(F_x = 6 \, \text{N}\) and \(F_y = -8 \, \text{N}\).
- Therefore,
\[ |\vec{F}| = \sqrt{(6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, \text{N} \]

3. **Use Newton's second law to find the mass**:
- According to Newton's second law:
\[ \vec{F} = m \cdot \vec{a} \]
- Rearranging this gives us:
\[ m = \frac{|\vec{F}|}{a} \]
- Substituting the values we have:
\[ m = \frac{10 \, \text{N}}{5 \, \text{m/s}^2} = 2 \, \text{kg} \]

4. **Conclusion**:
- The mass of the body is \(2 \, \text{kg}\).