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 uniform velocity
C. in equilibrium
D. moving with an acceleration

Explanation

To solve the problem, we need to analyze the forces acting on the body and determine the resultant force. Here’s a step-by-step breakdown:

### Step 1: Identify the Forces
We have three forces acting on the body:
- Force A = 50 N
- Force B = 30 N
- Force C = 15 N

### Step 2: Check the Condition for Equilibrium
For the body to be in equilibrium (i.e., at rest or moving with uniform velocity), the net force acting on it must be zero. This means that the vector sum of all forces must equal zero.

### Step 3: Apply the Triangle Inequality
To check if these forces can be in equilibrium, we can use the triangle inequality theorem. According to this theorem, for three forces to be in equilibrium, the sum of the magnitudes of any two forces must be greater than the magnitude of the third force.

Let's check:
- Compare Force A (50 N) with the sum of Forces B and C:
\[ 50 \text{ N} > (30 \text{ N} + 15 \text{ N}) = 45 \text{ N} \]
This condition is satisfied, indicating that Force A is greater than the sum of Forces B and C.

### Step 4: Conclusion from Triangle Inequality
Since one force (50 N) is greater than the sum of the other two forces (30 N + 15 N = 45 N), these forces cannot form a closed triangle. Therefore, they cannot be in equilibrium.

### Step 5: Determine the Motion of the Body
Since the forces do not balance out to zero, the body will not be at rest or moving with uniform velocity. Instead, it will experience a net force and will therefore accelerate in the direction of the resultant force.

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