Final answer:
The tension, 'T', must be measured in newtons (N) in order to ensure that the mass, 'm', is measured in grams (g). The tension T in the formula for calculating mass using the tension and length of a string must be measured in gram·centimeter/s² (g·cm/s²) to obtain mass in grams.
Step-by-step explanation:
The tension, 'T', must be measured in newtons (N) in order to ensure that the mass, 'm', is measured in grams (g). In the given formula, T.Lm = 12y, the tension 'T' is in newtons (N) and the mass 'm' is in kilograms (kg).
The tension T in the formula for calculating mass using the tension and length of a string must be measured in gram·centimeter/s² (g·cm/s²) to obtain mass in grams.
To ensure that the mass m is measured in grams when using the formula T × L / 12 (y = velocity of the wave in centimeters per second, and L is the length of the string in centimeters), the tension T must be measured in a unit that is compatible with grams and centimeters. Since tension is typically measured in newtons (N), and 1 newton is equal to 1 kg·m/s2, we need to convert this to a unit involving grams and centimeters.
To do this, remember that 1 kg = 1000 grams and 1 m = 100 centimeters. Therefore, 1 N can be converted to gram·centimeter/s2 (g·cm/s2) by calculating 1 N = 1000 g × (100 cm/s2) = 100,000 g·cm/s2. By measuring tension in g·cm/s2, the resulting mass will be in grams.