Which quantity and unit are INCORRECTLY paired?

A. Quantity: F Unit: kg m/s
B. Quantity: J Unit: N·s
C. Quantity: W Unit: J
D. Quantity: P Unit: W
E. Quantity: E Unit: kg m2/s2

My answer is A.

Which of these quantities is incorrectly paired with its S.I. unit?

To determine which quantity and unit are incorrectly paired, we need to understand the correct relationships between the different quantities and units.

A. Quantity: F Unit: kg m/s
The quantity is force represented by the symbol "F." The unit is given as "kg m/s." This is a valid representation for force according to Newton's second law, which states that force is equal to mass multiplied by acceleration. The standard unit for force is a newton (N), which is equivalent to kg m/s^2. Therefore, this pairing is correct.

B. Quantity: J Unit: N·s
The quantity is work or energy represented by the symbol "J." The unit is given as "N·s." This pairing is correct. Work, measured in joules (J), is equal to the product of force (measured in newtons) and displacement (measured in meters). Since force is measured in newtons (N), multiplying it by displacement measured in meters (s) results in the unit N·s, which is equal to joules.

C. Quantity: W Unit: J
The quantity is power represented by the symbol "W." The unit is given as "J." This pairing is also correct. Power, measured in watts (W), is defined as the rate at which work is done or energy is transferred. Since work is measured in joules (J) and power is the amount of work done per unit time, it is correct to have the unit of power expressed as joules per second (J/s) or watts (W).

D. Quantity: P Unit: W
The quantity is power represented by the symbol "P." The unit is given as "W." This pairing is correct. Both the quantity and unit represent power, measured in watts (W), as discussed in the previous explanation.

E. Quantity: E Unit: kg m^2/s^2
The quantity is energy represented by the symbol "E." The unit is given as "kg m^2/s^2." This is a valid representation for energy according to the standard unit for energy, which is the joule (J). The unit kg m^2/s^2 is equivalent to joules, so this pairing is also correct.

Therefore, all the quantity and unit pairings are correctly paired. None of the choices are incorrectly paired.