When three forces of `50 N, 30 N and 15 N` act on body, then the boy is

Options

A. At rest
B. Moving with a uniform velocity
C. In equilibrium
D. Moving with an acceleration

Explanation

To solve the problem of determining the state of a body acted upon by three forces of 50 N, 30 N, and 15 N, we will follow these steps:

### Step 1: Identify the Forces
We have three forces acting on a body:
- \( F_1 = 50 \, \text{N} \)
- \( F_2 = 30 \, \text{N} \)
- \( F_3 = 15 \, \text{N} \)

### Step 2: Apply the Triangle Inequality Theorem
To determine if the body is in equilibrium, we need to check if these forces can form a closed triangle. According to the triangle inequality theorem, for any three sides \( a, b, c \) of a triangle, the following must hold:
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

### Step 3: Check the Inequalities
Let's assign the forces:
- \( a = 50 \, \text{N} \)
- \( b = 30 \, \text{N} \)
- \( c = 15 \, \text{N} \)

Now, we check the inequalities:
1. \( 30 + 15 = 45 \) which is **not greater** than \( 50 \) (fails)
2. \( 50 + 15 = 65 \) which is **greater** than \( 30 \) (succeeds)
3. \( 50 + 30 = 80 \) which is **greater** than \( 15 \) (succeeds)

Since the first inequality fails, the forces cannot form a triangle.

### Step 4: Conclusion on Net Force
Since the forces do not satisfy the triangle inequality, they cannot be in equilibrium. Therefore, the net force acting on the body is not zero.

### Step 5: Determine the State of Motion
If the net force is not zero, the body will not be at rest or moving with uniform velocity. Instead, it will be moving with an acceleration due to the unbalanced forces acting on it.

### Final Answer
The body is moving with an acceleration.

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