Question

In a pulley system, two blocks are connected by a string over a frictionless pulley. If tensions \(T_1\) and \(T_2\) are given in two segments of the string, what is their relation?

• A. \( T_1 = T_2 \)
• B. \( T_1>T_2 \)
• C. \( T_1<T_2 \)
• D. Depends on masses only

Hint:

Tension only changes across a pulley if the pulley has mass and friction (which requires torque to rotate). In most introductory physics problems, unless stated otherwise, assume the tension is uniform.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
In classical mechanics, we often use the "Ideal String" and "Ideal Pulley" approximations. An ideal string is massless and inextensible, and an ideal pulley is frictionless and massless.

Step 2: Detailed Explanation
1. A string is considered a medium to transmit force. 2. If the string is massless, the net force on any segment of the string must be zero (otherwise, it would have infinite acceleration since \(a = F/m\)). 3. If the pulley is frictionless, it does not offer any resistive torque to the string. 4. Because the string is continuous and the pulley is frictionless, the magnitude of the tension remains constant throughout the entire length of the string connecting the two masses. 5. Therefore, the tension in the segment on the left (\(T_1\)) must be equal to the tension in the segment on the right (\(T_2\)).

Step 3: Final Answer
The relation is \( T_1 = T_2 \).