Question

A weightless spring scale is attached to two equal weights as shown below. The reading on the scale will be

       A) 0.
       B) W.
       C) 2W.
       D) (1/2)W.
       E) W^2.

Answer 1

The figure is not shown here, so let us assume weights of W is placed on both the ends.

The scale reads the only tension in the string. The tension in the string is W. This is the force the string must exert up on either of the weight W at either end of the string.

No acceleration or movement, so the net force on the spring is zero. Likewise, the total force on either of the weight W is also zero. But this is another question. The spring scale does not measure the total force. The spring scale simply measures the tension, the magnitude of the force exerted by the string

To prove this let us consider that a weight of W is attached to the one end of the spring. To balance the spring force of exactly W has to be exerted to the other end. This force is usually exerted by the person holding the spring, etc. But here there's nothing else holding the spring, we kept another equal weight W. Needless to say that the spring doesn't realize where the force comes from. The only thing that it knows is that it feels a weight of W and so that is its reading

So option B