A force of X Newton is acting on a body towards the left. The body moves towards the right, with a force much smaller than X Newtons. Which of these other forces must also have acted on the body?

Options

A. Force of X Newton towards the left
B. Force of X Newton towards the right
C. Force less than X Newton towards the left
D. Force greater than X Newton towards the right.

Answer

To solve the problem, we need to analyze the forces acting on the body and determine what additional force must be present for the body to move in the direction opposite to the applied force. Here’s a step-by-step breakdown:

### Step 1: Identify the forces acting on the body
- We have a force \( F_1 \) acting on the body towards the left, which is given as \( X \) Newtons.
- The body is moving towards the right with a force \( F_2 \) that is much smaller than \( X \) Newtons.

### Step 2: Understand the motion of the body
- The body is moving to the right, which means there must be a net force acting on it in the right direction. This net force must overcome the leftward force \( F_1 \).

### Step 3: Apply Newton's Second Law
- 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 (\( F_{net} = m \cdot a \)).
- For the body to move to the right, the net force acting on it must be greater than zero. Therefore, we can express this as:
\[ F_{net} = F_2 + F_3 - F_1 > 0 \]
where \( F_3 \) is the additional force acting on the body towards the right.

### Step 4: Rearranging the equation
- Rearranging the inequality gives us:
\[ F_2 + F_3 > F_1 \]
- Since \( F_1 = X \) Newtons, we can write:
\[ F_2 + F_3 > X \]

### Step 5: Determine the conditions for \( F_3 \)
- Given that \( F_2 \) is much smaller than \( X \), for the inequality \( F_2 + F_3 > X \) to hold true, \( F_3 \) must be sufficiently large.
- Thus, we can conclude that:
\[ F_3 > X - F_2 \]
- Since \( F_2 \) is very small compared to \( X \), we can simplify this to:
\[ F_3 > X \]

### Step 6: Conclusion
- Therefore, the additional force \( F_3 \) must be greater than \( X \) Newtons and must act towards the right for the body to move in that direction.

### Final Answer
The force that must also have acted on the body is a force greater than \( X \) Newtons acting towards the right.

---