Question

A book with many printing errors contains four different formulae for the displacement $y$ of a particle undergoing a certain periodic motion. Rule out the wrong formula on dimensional ground.
( $a=$ maximum displacement of the particle,
$v=$ speed of the particle, $T=$ time period of motion)

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

Answer 1

Answer: (B)

The argument of a trigonometric function must
be dimensionless. Further $[y]$ is not equal to $\left[\frac{a}{T}\right]$