Two blocks of equal masses are tied with a light string passing over a massless pulley (Assuming frictionless surfaces). The acceleration of the centre of mass of the two blocks is (Given ):
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Official Solution
Correct Option: (2)
Step 1: Understanding the problem The two blocks are placed on an inclined plane with angles and . The forces acting on them include their weights and the tension in the string. Step 2: Setting up equations of motion The components of gravitational force along the incline for each mass are:
Since the masses are equal, the net force acting on the system is:
Step 3: Calculating acceleration of the system Applying Newton’s second law:
Substituting :
Step 4: Final computation
Rearranging,
Thus, the acceleration of the centre of mass of the two blocks is:
