On applying force to the centre of mass of a body one of the following is present in the body?

Options

A. rotation
B. inear acceleration
C. angular velocity
D. angular acceleration

Answer

To solve the question, "On applying force to the center of mass of a body, one of the following is present in the body?", we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Concept of Center of Mass**:
- The center of mass (COM) of a body is a point where the mass of the body can be considered to be concentrated for the purpose of analyzing translational motion. When a force is applied at this point, it affects the motion of the entire body.

**Hint**: Remember that the center of mass is crucial for understanding how forces affect an object's motion.

2. **Applying Force at the Center of Mass**:
- When a force \( F \) is applied at the center of mass, according to Newton's second law, the body will experience linear acceleration. The equation \( F = m \cdot a \) applies, where \( m \) is the mass of the body and \( a \) is the acceleration of the center of mass.

**Hint**: Recall Newton's second law and how it relates force, mass, and acceleration.

3. **Effects on Angular Motion**:
- If the force is applied at the center of mass, there is no torque generated about the center of mass. Torque (\( \tau \)) is calculated as \( \tau = r \times F \), where \( r \) is the distance from the axis of rotation to the point where the force is applied. Since \( r = 0 \) when the force is applied at the center of mass, the torque is zero.

**Hint**: Understand the relationship between torque and angular motion; zero torque means no angular acceleration.

4. **Conclusion on Motion**:
- Since there is no torque, there will be no angular acceleration or angular velocity. The body will not rotate; it will only translate. Therefore, the only effect of applying a force at the center of mass is linear acceleration.

**Hint**: Focus on the distinction between linear and angular motion when forces are applied at different points.

5. **Final Answer**:
- The correct statement is that applying a force to the center of mass of a body results in linear acceleration of the body.

### Summary:
When a force is applied at the center of mass of a body, the body experiences linear acceleration, but there is no angular acceleration or angular velocity due to the absence of torque.