Dimensions: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

For SHM, \(x=A\omega\), \(y=\frac{\omega}{2\pi}\), \(z=A\omega^2\). Thus, \(\frac{xy}{z} = \frac{(A\omega)(\omega/(2\pi))}{(A\omega^2)} = \frac{1}{2\pi}\), which is a constant. So (A) is true. The dimensions are \([x]=LT^{-1}\), \([y]=T^{-1}\), \([z]=LT^{-2}\), making \([xy/z]=1\), dimensionless. So (R) is true. However, being dimensionless does not explain why it's a constant.