Final answer:
The time for block B to separate from block A on a frictionless surface when a 10 N force is applied can be calculated using Newton's second law and kinematic equations, leading to approximately 0.447 seconds.
Step-by-step explanation:
The question relates to the concept of Newton's laws of motion and involves calculating the time for block B to separate from block A on a frictionless surface when a horizontal force is applied. To solve this problem, we need to apply Newton's second law of motion to find the acceleration of block A and use kinematic equations to determine the time for block B to traverse the length of block A and separate.
Given the total force applied and the mass of block A, we can calculate the acceleration (a) using the formula a = F/m, where F is 10 N and m is 5 kg. Hence, the acceleration is 2 m/s2. Using one of the kinematic equations, s = ut + 1/2 at2, with the initial velocity u = 0, we can determine the time 't' it takes for the block B to move 20 cm (0.2 meters) on block A. Solving for 't' gives us t = sqrt(2s/a), substituting the values, we get t = sqrt(2*0.2/2), which simplifies to t = sqrt(0.2) seconds, or approximately t = 0.447 seconds, none of the options (a-d) matches this value.