Which of the following is the correct dimensional formula for frequency? (2021)
Practice Questions
Q1
Which of the following is the correct dimensional formula for frequency? (2021)
[M^0 L^0 T^-1]
[M^0 L^1 T^-1]
[M^1 L^0 T^-1]
[M^0 L^0 T^1]
Questions & Step-by-Step Solutions
Which of the following is the correct dimensional formula for frequency? (2021)
Step 1: Understand what frequency means. Frequency is how often something happens in a certain amount of time.
Step 2: Recall the basic formula for frequency. Frequency (f) is defined as the number of cycles (n) per unit time (T), which can be written as f = n/T.
Step 3: Identify the dimensions of the components in the formula. The number of cycles (n) is a count and has no dimensions, so it is [M^0 L^0 T^0].
Step 4: Determine the dimensions of time (T). Time has the dimensional formula [M^0 L^0 T^1].
Step 5: Combine the dimensions from the frequency formula. Since frequency is cycles per time, we have: [M^0 L^0 T^0] / [M^0 L^0 T^1].
Step 6: Simplify the dimensional formula. This results in [M^0 L^0 T^-1], which means frequency has no mass or length dimensions and has a negative exponent for time.
