A body of mass `10kg` is acted upon by two per pendicular forces `6N` and `8N`. The resultant ac-celeration of the body is .

Options

A. `1ms^(-2)" at angle of tan"^(-1)((3)/(4))w.r.t. 8N "force"`
B. `0.2ms^(-2)" at angle of tan"^(-1)((3)/(4))w.r.t. 8N "force"`
C. `1ms^(-2)" at angle of tan"^(-1)((4)/(3))w.r.t. 8N "force"`
D. `0.2ms^(-2)" at angle of tan"^(-1)((4)/(3))w.r.t. 8N "force"`

Explanation

To find the resultant acceleration of a body of mass 10 kg acted upon by two perpendicular forces of 6 N and 8 N, we can follow these steps:

### Step 1: Identify the forces
We have two forces:
- \( F_1 = 6 \, \text{N} \)
- \( F_2 = 8 \, \text{N} \)

### Step 2: Calculate the resultant force
Since the forces are perpendicular to each other, we can use the Pythagorean theorem to find the resultant force \( F_r \):
\[ F_r = \sqrt{F_1^2 + F_2^2} \]
Substituting the values:
\[ F_r = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, \text{N} \]

### Step 3: Use Newton's second law to find acceleration
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
\[ F = m \cdot a \]
Rearranging for acceleration \( a \):
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{10 \, \text{N}}{10 \, \text{kg}} = 1 \, \text{m/s}^2 \]

### Step 4: Conclusion
The resultant acceleration of the body is:
\[ \boxed{1 \, \text{m/s}^2} \]

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