A Mass M₁ Is Connected by a Light String That

question 72

Multiple Choice

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR². If m₁ is 2.00 kg, m₂ is 1.00 kg, M is 4.00 kg, and the angle is 60.0 degrees, then what is the acceleration of m₁?

• A) 3.98 m/s² down
• B) 3.27 m/s² down
• C) 3.15 m/s² down
• D) 2.94 m/s² down
• E) 1.64 m/s² down

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Definitions:

Ability-To-Pay Principle

The concept that taxes should be levied according to an individual's or entity's ability to bear them, typically resulting in higher earners paying more taxes.

Lump-Sum Taxes

Taxes that are a fixed amount, not dependent on the taxpayer's income or activities, thus they do not distort economic decisions.

Economic Efficiency

A condition where every resource is optimally allocated to serve each individual or entity in the best way while minimizing waste and inefficiency.

Ability-To-Pay Principle

The ability-to-pay principle in taxation suggests that taxes should be levied based on an individual's or entity's capacity to pay, meaning those with higher income should pay more.