Question

Which of the following statements regarding the damping force of a damped oscillator is NOT correct? Options:

• A. Damping force depends on the nature of the surrounding medium.
• B. Damping force is generally proportional to the velocity of the body making oscillations.
• C. Damping force acts in the direction of the velocity of the body.
• D. Ratio of the damping force and velocity of the body depends on the size and shape of the body.

Hint:

The direction of the damping force is always opposite to the motion of the object, making it a resistive force that reduces the object's kinetic energy.

Answer 1

The Correct Option is C

Statement (1): Damping force does depend on the medium through which the object is moving. A denser medium creates more resistance, leading to a greater damping force. 
Statement (2): This is correct. The damping force is generally proportional to the velocity of the body, as described by \( F_{\text{damping}} = -b v \), where \( b \) is a damping coefficient and \( v \) is the velocity. 
Statement (3): This statement is incorrect. The damping force always acts opposite to the direction of the velocity of the body, not in the same direction. 
Statement (4): This is true. The damping force also depends on factors such as the size and shape of the body because they influence the drag force in the medium. 
Conclusion: Statement (3) is incorrect, making it the right answer. The correct answer is (3). 
Final Answer: \[ \boxed{\text{Damping force acts in the direction of the velocity of the body.}} \]