Which of the following is dimensionlessa.volume/areab.velocity/accelerationc.energy/workd.force/acceleration

To determine which of the options is dimensionless, we need to understand the concept of dimensionality. In physics, dimensions are used to describe the physical quantities involved in a problem. These dimensions can include length, time, mass, and so on.

To check if a quantity is dimensionless, we need to examine the units of each term in the given options.

a. volume/area: Volume is measured in cubic units (e.g., cubic meters), while area is measured in square units (e.g., square meters). Therefore, the ratio of volume to area does not cancel out any units, so it is not dimensionless.

b. velocity/acceleration: Velocity is measured in units of length per time (e.g., meters per second), while acceleration is measured in units of length per time squared (e.g., meters per second squared). Again, the ratio of velocity to acceleration does not cancel out any units, so it is not dimensionless.

c. energy/work: Energy is measured in units of joules, while work is also measured in units of joules. Since the units cancel out in this case, the ratio of energy to work is dimensionless.

d. force/acceleration: Force is measured in units of newtons, while acceleration is measured in units of meters per second squared. Similar to the previous options, the ratio of force to acceleration does not cancel out any units, so it is not dimensionless.

Therefore, the correct answer is c. energy/work, as it is the only option that results in a dimensionless quantity.