Two objects are connected with a string. In the quantitative treatment of the problem we assume that the string exerts a tension force of magnitude T on each of the two objects. What do we need to assume for this assumption to be valid?
a) the string may hang loose between the objects
b) the string does not pass over a pulley
c) the string is massless
d) the two objects are not on a collision course with each other
e) none of the above
The assumption that the string exerts a tension force of magnitude T on each of the two objects is valid when the string is massless. Therefore, option c) "the string is massless" is the correct assumption for this situation.
To see why, we need to consider the forces involved. In this scenario, the tension force in the string is assumed to be the same everywhere along its length. If the string has mass, it would experience a gravitational force due to its own weight, which would cause the tension to vary along its length. This would result in different tension forces acting on the two objects, violating the assumption made in the problem.
By assuming that the string is massless, we are simplifying the problem by neglecting the effect of gravity on the string itself. This assumption allows us to consider the tension force as constant throughout the string, enabling us to analyze the forces on the two connected objects in a straightforward manner.
Hence, the valid assumption for this situation is that the string is massless (option c).