Question

When an object of weight W is suspended from the center of a massless string as shown above, the tension at any point in the string is...

A. W
B. W/2
C. 2W
D. 0

Answer 1

The correct answer is (A)
`\( W \)`. The tension in the string is equal to the weight of the object, and it remains constant throughout the length of the string.

When an object of weight
`\( W \)` is suspended from the center of a massless string, the system is in equilibrium. In this case, the tension in the string is constant throughout, and it equals the weight of the object.

Here's the reasoning:

1. At the center of the string:

- The object is suspended at the center of the string.

- In equilibrium, the net force acting on the object is zero.

- The only forces acting on the object are its weight
`(\( W \))` acting downward and the tension in the string.

- Since the object is not accelerating vertically, the tension in the string must exactly balance the weight of the object.

- Therefore, the tension
`(\( T \))` in the string is equal to the weight of the object
`(\( W \))`.

2. Throughout the string:

- The string is assumed to be massless, meaning its mass is negligible compared to the mass of the object.

- In a massless string, the tension is transmitted undiminished throughout the entire length of the string.

- This means that the tension at any point in the string is the same as the tension at any other point.

Therefore, the correct answer is (A)
`\( W \)`. The tension in the string is equal to the weight of the object, and it remains constant throughout the length of the string.

Answer 2

The tension at any point in a string supporting a stationary object of weight W is equal to W, as the upward tension and downward weight force balance each other.

Step-by-step explanation:

When an object of weight W is suspended from the center of a massless string, the tension at any point in the string is W. This can be understood by applying Newton's second law. If the object is stationary, its acceleration is zero, which implies that the net force acting on the object must also be zero.

Given that the only forces acting on the object are its weight (W) pointing downward and the tension (T) in the string pointing upward, these two forces must balance each other out.

Thus, the tension in the string is equal to the weight of the object. By substituting the expression for weight (mg), where m is the mass and g is the acceleration due to gravity, we confirm that the tension T equals mg. Therefore, the tension at any point in the string is equal to W, demonstrating that the correct answer is A. W.