Final answer:
The common acceleration of the two blocks with masses 1.0 kg and 3.0 kg when a force of 12 N is applied is calculated to be 3.0 m/s² using Newton's second law, which is not listed in the provided options.
Step-by-step explanation:
The student asked a question regarding the common acceleration of two blocks connected to each other and subject to an externally applied force on a frictionless surface. To solve this, we use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F = ma). Considering both blocks as a single system, we have a total mass of 1.0 kg + 3.0 kg = 4.0 kg. The force applied is 12 N.
We can calculate the acceleration as follows:
- Calculate the total mass of the system: mtotal = mA + mB = 1.0 kg + 3.0 kg = 4.0 kg.
- Use Newton's second law to find the acceleration: a = F / mtotal = 12 N / 4.0 kg = 3.0 m/s².
Therefore, the common acceleration of the two blocks is 3.0 m/s², which is not represented in the options provided (a)2m/s² (b)4m/s² (c)6m/s² (d)8m/s², indicating there might have been an error in either the question or the options provided.