Help understand how to solve question 4. ---**Question:**
4. Block A of mass m rests on the plank B of mass 3m which is free to slide on a frictionless horizontal surface. The coefficient of friction between the block and plank is 0.2. If a horizontal force of magnitude 2mg is applied to the plank B, the acceleration of A relative to the plank and relative to the ground respectively, are:
**Options:**
(a) 0, g/2
(b) 0, 2g/3
(c) 3g/5, g/5
(d) 2g/5, g/5
**Diagram Description:**
* Type: Schematic diagram illustrating a physical setup.
* Elements:
* Block A: A rectangular block labeled "A" is shown resting on top of Plank B. It is labeled with mass "m".
* Plank B: A larger rectangular plank labeled "B" is shown below Block A. It is labeled with mass "3m".
* Surface: Plank B is shown resting on a horizontal surface represented by horizontal lines with small diagonal lines indicating it is a surface. This surface is described as frictionless in the text.
* Applied Force: A horizontal arrow points to the right, applied to Plank B. It is labeled with "2mg".
* Relative Positions: Block A is centered on top of Plank B. Plank B is resting on the horizontal surface.
* Direction: The applied force is horizontal and acts towards the right.
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Let's analyze this friction problem step by step. We have block A with mass m resting on plank B with mass 3m. A horizontal force of 2mg is applied to plank B. The coefficient of friction between A and B is 0.2. We need to find the acceleration of A relative to the plank and relative to the ground.