Two blocks of mass M kg and 2,5 kg respectively are connected by a light,inextensible string.The string runs over a light,frictionless pulley

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Step 1: Draw a diagram

To better understand the setup, it's helpful to draw a diagram. In this case, you can draw two blocks connected by a string, with the string running over a pulley.

Step 2: Identify the given information
From the question, we know the following:
- The mass of the first block is M kg.
- The mass of the second block is 2.5 kg.
- The string connecting the two blocks is light (meaning it has negligible mass) and inextensible (meaning it doesn't stretch).
- The pulley is light and frictionless.

Step 3: Determine the forces acting on each block
For the first block with mass M kg, there are two forces acting on it:
- Weight: The force due to gravity acting downward. The magnitude of the weight is equal to the mass of the block multiplied by the acceleration due to gravity (9.8 m/s^2).
- Tension: The tension in the string that pulls the block upward. The magnitude of the tension is the same throughout the string.

For the second block with mass 2.5 kg, there are two forces acting on it as well:
- Weight: The force due to gravity acting downward. Again, the magnitude of the weight is equal to the mass of the block multiplied by the acceleration due to gravity.
- Tension: The tension in the string that pulls the block downward. As the block moves downward, the tension in the string will be slightly less than the weight of the block to provide the net force necessary for downward motion.

Step 4: Determine the direction of motion
Based on the setup, we can see that the second block is being pulled downward, while the first block is being pulled upward. This indicates that the system will accelerate in the direction of the second block.

Step 5: Apply Newton's second law
For the first block, Newton's second law can be written as:
Tension - Weight of the first block = Mass of the first block × Acceleration

For the second block, Newton's second law can be written as:
Weight of the second block - Tension = Mass of the second block × Acceleration

Step 6: Solve the equations
You can use the system of equations to solve for the acceleration and the tension in the string.

The two equations are:
Tension - M × 9.8 = M × a (equation 1)
2.5 × 9.8 - Tension = 2.5 × a (equation 2)

Simplifying equation 2, we get:
24.5 - Tension = 2.5 × a

Now we have two equations with two variables (tension and acceleration), and we can solve them simultaneously to find their values.

To solve this problem, we need to consider the forces acting on each block separately and apply Newton's second law of motion.

Let's denote the mass of the first block as M kg and the mass of the second block as 2.5 kg.

For the first block (M kg):
- The weight of the block is given by W1 = M * g, where g is the acceleration due to gravity.
- The tension in the string pulling the first block upwards is denoted as T1 (acting in the upward direction).
- As there is no friction in the system, the magnitude of the tension force T1 is equal to the weight of the block W1.
- Thus, T1 = M * g.

For the second block (2.5 kg):
- The weight of the block is given by W2 = 2.5 * g.
- The tension in the string pulling the second block downwards is denoted as T2 (acting in the downward direction).
- As there is no friction in the system, the magnitude of the tension force T2 is equal to the weight of the block W2.
- Thus, T2 = 2.5 * g.

Since the blocks are connected by a light, inextensible string and run over a light, frictionless pulley, the tension forces T1 and T2 are equal in magnitude.

Therefore, T1 = T2 = T.

Now, we can apply Newton's second law to each block:
- For the first block, the net force acting on it is T - W1. According to Newton's second law, we have:
T - W1 = M * a1, where a1 is the acceleration of the first block.
- For the second block, the net force acting on it is W2 - T. According to Newton's second law, we have:
W2 - T = m2 * a2, where a2 is the acceleration of the second block.

Since the magnitude of the tension forces T1 and T2 are equal, we can substitute T for both T1 and T2 in the above equations.

Now, we have a system of two equations with two unknowns (T and a1 or a2). Solving this system of equations will give us the values of T, a1, and a2.

It's important to note that in this system, the smaller mass block (2.5 kg) will accelerate downwards, while the larger mass block (M kg) will accelerate upwards.

To solve this system of equations, you'll need to assign values to the masses (M and 2.5 kg) and the acceleration due to gravity (g), and then solve for T, a1, and a2 using the equations mentioned above.