When a6 gram mass is attached to a spring hanging vertically, the spring is stretched to a total length of 24 centimeters. When a 10 gram mass is attached to the spring (and only the 10 gram mass), the spring is stretched to a total length of 36 centimeters. What is the total length of the spring when a 12 grammass is attached to it? Elimination Tool Select one answer A 18cm 15 cm B 36 cm D 30 cm E 42cm

## Step1: Identify the key relationships### The problem involves forces and Hooke's Law, which states that the force exerted by a spring is proportional to its extension. Hooke's Law is given by , where is the spring constant and is the extension of the spring.## Step2: Calculate forces for given masses### Convert masses to forces using (where ).For a 6 gram mass ( ): For a 10 gram mass ( ): ## Step3: Determine the extension for each mass### Subtract the original length of the spring (assumed constant) from the given total lengths.Extension for 6 gram mass: Extension for 10 gram mass: ## Step4: Calculate the spring constant (k)### Use Hooke's Law .For the 6 gram mass: Ensure consistency and check with the 10-gram mass: ## Step5: Calculate the spring constant and new extension accurately### As the calculations vary slightly, average : ## Step6: Calculate the new extension for a 12 gram mass ## Step7: Calculate the total length of the spring