Assertion (A): Light year and wavelength have same dimensions.
Reason (R): Light year represent time while wavelength represent distance.
Both light year and wavelength represent distance and have the dimension \([L]\). Since light year represents distance and not time, R is false.
Assertion (A): Angle and strain are dimensionless.
Reason (R): Angle and strain have no unit.
Both angle and strain are ratios of like quantities and are dimensionless. However, angle has a unit (radian), so R is false.
Assertion (A): In SHM let \(x\) be the maximum speed, \(y\) the frequency of oscillation and \(z\) the maximum acceleration, then \(\frac{xy}{z}\) is a constant quantity.
Reason (R): This is because \(\frac{xy}{z}\) becomes a dimensionless quantity
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.