# 2.14 A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :(a) $y = a sin 2\pi t/T$(b) $y = a sin vt$(c) $y = (a/T) sin\ t/a$(d) $y = ( a\sqrt{2}) (sin 2\pi t / T+ cos 2\pi t / T )$(a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.

Ground rules:

$\\sin\Theta , cos\Theta \ are\ DIMENSIONLESS.\ \\ and\ \Theta\ must\ be\ dimensionless$

[y] = L  ($M^0 L^1 T^0$)

[a] = L

[v] = $\dpi{80} LT^{-1}$

[t/T] is Dimenionless.

(a) The dimensions on both sides are equal, the formula is dimensionally correct.

(b) $\dpi{80} \because$ [vt] = ($\dpi{80} LT^{-1}$)(T) = L ($\dpi{100} \therefore \Theta$ is not dimensionless)

The formula is dimensionally incorrect

(c) [a/T] = (L)/(T)

It is dimensionally incorrect, as the dimensions on both sides are not equal.

(d) The dimensions on both sides are equal, the formula is dimensionally correct. (Don't get confused by summation of trigonometric functions !)

## Related Chapters

### Preparation Products

##### JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
##### Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
##### Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
##### Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-