Q. Two blocks of masses 4 kg and 2 kg are placed on a smooth horizontal surface and connected by a light string. A force of 18 N is applied on the 4 kg block. (a) Find the acceleration of the system. (b) What is the tension in the string? Question Visualisers. Where a complicated question is detail visualized. Grade 11, topic - law of motion.

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Let's analyze a two-block system problem. We have two blocks with masses 4 kg and 2 kg connected by a light string on a smooth horizontal surface. A force of 18 N is applied to the 4 kg block. We need to find the acceleration of the system and the tension in the string. The key points are that the surface is frictionless, meaning no friction forces act on the blocks, and the string is light, meaning it has negligible mass. Now let's analyze the system. Since the blocks are connected by an inextensible string, they must move together with the same acceleration. We can treat this as a single system with total mass of 6 kg. The key insight is that only external forces affect the system's acceleration. The 18 N force is the only external horizontal force acting on the system. Internal forces like string tension don't change the overall motion of the system, they only determine how the external force is distributed between the blocks. Now let's calculate the system acceleration using Newton's second law. We apply the equation F net equals total mass times acceleration. Substituting our values: 18 equals 4 plus 2 times a, which simplifies to 18 equals 6a. Solving for acceleration, we get a equals 18 divided by 6, which equals 3 meters per second squared. This means both blocks accelerate together at 3 meters per second squared to the right. Now let's analyze each block individually using free body diagrams. For the 4 kg block, we have the applied force of 18 N acting to the right and the tension T acting to the left. For the 2 kg block, only the tension T acts to the right. The key insight is that the tension is the same throughout the light string. Using Newton's second law for each block: for block 1, 18 minus T equals 4 times a, and for block 2, T equals 2 times a. These equations will help us find the tension. Now let's calculate the string tension using two different methods. Method 1: Using block 2, we apply Newton's second law. T equals m2 times a, which is 2 times 3, giving us T equals 6 N. Method 2: Using block 1, we have 18 minus T equals m1 times a, so 18 minus T equals 4 times 3, which is 12. Therefore, T equals 18 minus 12, which is 6 N. Both methods give us the same result, confirming that the tension in the string is 6 N.