Question

1. true/false: (4 points)

i. the period of oscillation for a pendulum is independent of the mass of the pendulum. (.........)
ii. fluid flowing through a pipe with a high average velocity has a low volumetric flow rate. (.........)
iii. effective interest rate is the stated or the quoted interest rate. (.........)
iv. in the control charts, one of the patterns for poor quality is when any datapoint plots outside of ucl or lcl. (.........)

1. multiple - choice: (3 points)

Explanation:

• i: The formula for the period of a simple pendulum is \(T = 2\pi\sqrt{\frac{L}{g}}\), where \(L\) is the length of the pendulum and \(g\) is the acceleration due to gravity. There is no mass term in this formula, so the period is independent of the mass of the pendulum.
• ii: Volumetric flow rate \(Q=A\times v\), where \(A\) is the cross - sectional area of the pipe and \(v\) is the average velocity of the fluid. If the average velocity \(v\) is high (assuming the cross - sectional area \(A\) is non - zero and constant), the volumetric flow rate \(Q\) will be high.
• iii: The stated or quoted interest rate is the nominal interest rate. The effective interest rate takes into account the compounding effect. For example, if the nominal rate is \(r\) and compounding is done \(n\) times a year, the effective rate \(i=(1 +\frac{r}{n})^n-1\).
• iv: In control charts, the Upper Control Limit (UCL) and Lower Control Limit (LCL) are used to determine if a process is in control. If a data point plots outside of UCL or LCL, it is an indication of a special cause of variation, which is a pattern for poor quality (assuming the control limits are calculated correctly).

Answer:

i. True
ii. False
iii. False
iv. True