A body of mass 5kg is acted upon by two perpendicular force 8N and 6N, find the magnitude and direction the acceleration

Options

A. `3 ms^(-2), theta=cos^(-1)(0.8) " from "8 m`
B. `2 ms^(-2), theta=cos^(-1)(0.6) " from "6 m`
C. `3 ms^(-2), theta=cos^(-1)(0.9) " from "6 m`
D. `5 ms^(-2), theta=cos^(-1)(0.81) " from "8 m`

Answer

To solve the problem, we need to find the magnitude and direction of the acceleration of a body of mass 5 kg acted upon by two perpendicular forces of 8 N and 6 N.

### Step-by-Step Solution:

1. **Identify the Forces**:
The two forces acting on the body are:
- \( F_1 = 8 \, \text{N} \) (acting in one direction)
- \( F_2 = 6 \, \text{N} \) (acting in a perpendicular direction)

2. **Calculate the Resultant Force**:
Since the forces are perpendicular, we can use the Pythagorean theorem to find the resultant force \( F_R \):
\[ F_R = \sqrt{F_1^2 + F_2^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{N} \]

3. **Calculate the Acceleration**:
Using Newton's second law, \( F = ma \), we can find the acceleration \( a \):
\[ a = \frac{F_R}{m} = \frac{10 \, \text{N}}{5 \, \text{kg}} = 2 \, \text{m/s}^2 \]

4. **Determine the Direction of the Acceleration**:
To find the direction of the acceleration, we can use trigonometric ratios. We can find the angle \( \theta \) that the resultant force makes with the horizontal axis (the direction of the 8 N force):
\[ \cos \theta = \frac{F_2}{F_R} = \frac{6}{10} = 0.6 \]
Therefore,
\[ \theta = \cos^{-1}(0.6) \]

5. **Final Result**:
- Magnitude of acceleration: \( 2 \, \text{m/s}^2 \)
- Direction of acceleration: \( \theta = \cos^{-1}(0.6) \)