Question

01 i. Is Equation 1 dimensionally homogenous? Provide your explanation. V = Vo + gt2 (Equation 1) time t has the unit of second, In Equation 1, v and vo stand for velocities having the units of and g, gravitational acceleration has the unit of g = 9.81" ii. Is Equation 2 dimensionally homogenous? Provide your explanation. v = vo + gt (Equation 2) In Equation 2, v and vo stand for velocities having the units of ", time thas the unit of hour, and g, gravitational acceleration has the unit of g = 9.815 iii. Is Equation 2 above valid? In other words, is it dimensionally homogenous and consistent in units? Provide your explanation. How should Equation (2) be written so that it is valid?

Answer 1

For this question, we'll first understand the difference between dimensions and units.

Dimensions - length, mass, weight, time etc

Units - kg, grams, hour, metres etc

Therefore, to find that the equation is homogeneous dimensionally, we substitute the values of the terms with respective dimensions.

Hence, the equation will be homogeneous ifa the terms have same dimensions.

(1) m=lenath mz - m = length o me lenger leneth - tine time go m = length 728=time r se [time? z) Acc. to eqn, mi may contain lenoth z lenoth & lenath Z od tine tine 8 mot dunensionally nomogenous

) Ace. to eqn . - m z mt m x hour = length allmoth + lenothx tim time time (tines Equis dimensionally revenous .

iii) In ii we can see that the equation is homogeneous dimensionally but not consistent in units.

Therefore, to make the equation valid i.e. make it consistent in units too, we change the unit of time from hours to seconds by

Seconds = hours x60x 60

Therefore,

&) m» вам на сьомг.) 8o En is dimensionally Колумдаипсош од well as consistent in units