A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:

( $a = maximum displacement of the particle$ , $v = speed of the particle$ , $T = time - period of motion$ ). Rule out the wrong formulas on dimensional grounds.

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Important Points to Remember in Chapter -1 - Units and Measurements from NCERT PHYSICS PART 1 TEXTBOOK FOR CLASS XI Solutions

1. Unit:

Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic standard called unit.

2. Fundamental Units:

S.No.	Physical Quantity	SI Unit	Symbol
$1$	Length	Metre	$M$
$2$	Mass	Kilogram	$K g$
$3$	Time	Second	$S$
$4$	Electric Current	Ampere	$A$
$5$	Temperature	Kelvin	$K$
$6$	Luminous Intensity	Candela	$C d$
$7$	Amount of Substance	Mole	$M o l$

3. Supplementary Units:

S.No.	Physical Quantity	SI Unit	Symbol
$1$	Plane Angle	radian	$r$
$2$	Solid Angle	Steradian	$S r$

4. Metric Prefixes:

S.No.	Prefix	Symbol	Multiplier
$1$	Centi	$c$	$10^{2}$
$2$	Milli	$m$	$10^{3}$
$3$	Micro	$μ$	$10^{6}$
$4$	Nano	$n$	$10^{9}$
$5$	Pico	$p$	$10^{12}$
$6$	Kilo	$K$	$10^{3}$
$7$	Mega	$M$	$10^{6}$

5. Errors in measurements:

(i) Values obtained from several measurements are $a_{1}, a_{2}, a_{3} \dots . a_{n}$ : Mean value $a_{m e a n} = \frac{a_{1} + a_{2} + \dots a_{n}}{n}$

(ii) Absolute error of a measurement $Δ a_{1} = a_{1} - a_{m e a n}$

(iii) Mean absolute error $Δ a_{m e a n} = \frac{Δ a_{1} + Δ a_{2} + . \dots . . Δ a_{n} .}{n}$

(iv) Any measurement we take for the physical quantity $a$ may lie between $a_{m e a n} + Δ a_{m e a n}$ and $a_{m e a n} - Δ a_{m e a n}$

(v) Relative error in $= \frac{Δ a_{m e a n}}{a_{m e a n}}$

(vi) Percentage error $= \frac{Δ a_{m e a n}}{a_{m e a n}} \times 100 %$

6. Combination of errors:

(i) If two physical quantities $A$ and $B$ have measured values $a \pm Δ a$ and $b \pm Δ b$ and if $Z = A + B$ and $Z$ is expressed as $z \pm Δ z$ , then $z = a + b$ and $Δ z = Δ a + Δ b$