7. In the pulley-block system shown, find the accelerations of A, B, C and the tension in the string. Assume the friction to be negligible and the string to be light and inextensible. The masses of the blocks are m, 2m and 3m respectively.

## Step 1: Identify the Forces on Each BlockFirst, we need to identify the forces acting on each block. For each block, there are two forces: the force due to gravity (which is the mass of the block times the acceleration due to gravity, ), and the tension in the string.## Step 2: Apply Newton's Second LawNext, we apply Newton's second law, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. For each block, we can write an equation that represents this law.## Step 3: Solve for the Accelerations and TensionFinally, we solve the equations we've written for the accelerations of blocks A, B, and C and the tension in the string.### For Block A:The forces acting on block A are the tension in the string (T) acting upwards and the force due to gravity acting downwards ( ). Applying Newton's second law gives us the equation:### ### For Block B:The forces acting on block B are the tension in the string (T) acting downwards and the force due to gravity acting upwards ( ). Applying Newton's second law gives us the equation:### ### For Block C:The forces acting on block C are the tension in the string (T) acting upwards and the force due to gravity acting downwards ( ). Applying Newton's second law gives us the equation:### Solving these three equations simultaneously gives us the accelerations of blocks A, B, and C and the tension in the string.