Question

Which of the following relations for the displacement of a partide undergoing simple harmonic motion is not correct dimensionally?

• A. $Y=a\sin \frac{2\pi t}{T}$
• B. $Y=a\cos \omega t$
• C. $Y=\frac{a}{T}\sin \left(\frac{t}{a}\right)$
• D. $Y=a\sqrt{2}(\sin \frac{2\pi t}{T}+\cos \frac{2\pi t}{T})$

Answer 1

Answer: (C)

$Y=\frac{a}{T}\sin \left(\frac{t}{a}\right)$

$\begin{array}{c}Y=\frac{a}{T}\sin \left(\frac{t}{a}\right)\\ Now,a\to meters\\ T\to seconds\\ a/T=m/s\to unitofvelocity\end{array}$

Dimensions on RHS must be displacement [L]. Arguments of sine and cosine are dimensionless. Hence, the option (c) is not correct.