Final answer:
For identical springs with negligible weight and identical objects, the extension of the springs will be the same. This is because the force applied by the objects and the resistance provided by the identical springs will be consistent across both springs, leading to equal extension.
Step-by-step explanation:
The lengths x1, x2, and x3 represent the extension of the springs. When a mass is attached to a spring, such as in this scenario, it stretches until it reaches a new equilibrium position where the force of gravity (acting downwards) is balanced by the spring force (acting upwards). This point of balance is dependent on two main factors: the stiffness of the spring (also known as the spring constant k) and the mass attached to the spring.
If we have identical springs and objects, the extension or compression in them will be equal for all springs involved. This is because the identical objects apply the same force due to gravity, and identical springs have the same intervening spring constant. Therefore, if the identical springs have insignificant weight, answering this particular physics problem, we could deduce that:
- (a) Spring A will have more extension than spring B. - Incorrect, assuming springs and weights are identical.
- (b) Spring B will have more extension than spring A. - Incorrect, assuming springs and weights are identical.
- (c) Both springs will have equal extension.
- (d) Both springs are equally stiff - True, by the premise of the problem.
Therefore the correct answer is (c) Both springs will have equal extension.