what is the answer---**Question Information:** * **Question Number and Source:** 116. < HKAL 1986 Paper I - 1 > **Diagram Description:** * **Type:** Physics system diagram. * **Elements:** * An inclined plane forming the base of a right-angled triangle. * The angle of inclination is labeled as 30° to the horizontal. * A rectangular block is placed on the inclined plane. The mass of this block is labeled as 4 kg. * A string is attached to the block on the plane, passes over a pulley located at the top edge of the inclined plane. * The pulley is depicted as a circle. * Another rectangular block is suspended vertically from the string after passing over the pulley. The mass of this block is labeled as 1 kg. * The string is shown connecting the two blocks via the pulley. **Question Stem:** An object of mass 4 kg is placed on a smooth plane inclined at 30° to the horizontal. It is connected by a light string passing over a frictionless pulley to another object of mass 1 kg, as shown above. Take g to be 10 m s⁻². If the system is released, the tension in the string will be **Options:** A. 12 N B. 15 N C. 18 N D. 25 N

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In this problem, we have a 4 kilogram block on an inclined plane at 30 degrees, connected by a string over a pulley to a 1 kilogram hanging block. We need to find the tension in the string when the system is released. Let's analyze the forces acting on each block. For the 4 kg block, gravity acts downward with a force of 40 Newtons. The component of gravity parallel to the incline is 20 Newtons, pulling the block down the incline. The tension in the string pulls the block up the incline. For the 1 kg block, gravity pulls it down with a force of 10 Newtons, while the tension pulls it upward. Now, let's apply Newton's Second Law to solve for the tension. For the 4 kg block moving down the incline, the net force equals mass times acceleration. The component of gravity down the incline is 20 Newtons, and the tension opposes this motion. So we get 20 minus T equals 4a. For the 1 kg hanging block moving upward, the tension pulls it up while gravity pulls it down. So T minus 10 equals 1a. Since the blocks are connected by a string, they have the same acceleration magnitude. From the second equation, we get a equals T minus 10. Substituting this into the first equation: 20 minus T equals 4 times (T minus 10), which gives us 20 minus T equals 4T minus 40. Rearranging, we get 60 equals 5T, so the tension T equals 12 Newtons. Therefore, the answer is A. Let's summarize what we've done. We had a 4 kilogram block on a plane inclined at 30 degrees, connected by a string over a pulley to a 1 kilogram hanging block. We needed to find the tension in the string when the system is released. We applied Newton's Second Law to both blocks. For the 4 kilogram block, the net force down the incline gave us the equation: 20 minus T equals 4a. For the 1 kilogram block moving upward, we got: T minus 10 equals a. Since the blocks are connected, they have the same acceleration magnitude. We substituted a equals T minus 10 into our first equation, which gave us 20 minus T equals 4 times T minus 40. Solving this equation, we got 60 equals 5T, so T equals 12 Newtons. Therefore, the correct answer is A: 12 Newtons. Let's verify our solution and understand the physical interpretation. We found that the tension in the string is 12 Newtons. Using this value, we can calculate the acceleration of the system. From our equation T minus 10 equals a, we get an acceleration of 2 meters per second squared. Let's check if this is consistent with the forces on each block. For the 4 kilogram block, the net force should equal mass times acceleration, which is 4 times 2, or 8 Newtons. The net force is also the component of gravity down the incline minus the tension, which is 20 minus 12, also equal to 8 Newtons. For the 1 kilogram block, the net force is 1 times 2, or 2 Newtons. This equals the tension minus the weight, which is 12 minus 10, also 2 Newtons. Physically, the system accelerates because the forces are unbalanced. The tension of 12 Newtons is between the weights of the two blocks, which makes sense because the heavier block pulls the lighter one upward. Let's summarize the key takeaways from this problem. First, when analyzing connected objects, it's important to identify all forces acting on each object separately. Second, apply Newton's Second Law to each object individually, writing F equals ma for each one. Third, for objects connected by a string over a pulley, the tension is the same throughout the string. Fourth, connected objects have the same magnitude of acceleration, though the direction may differ. Finally, the tension in a string is determined by the masses and forces in the entire system, not just by the hanging mass. In this problem, we found that the tension is 12 Newtons, which is option A.