Question

Hello !

Q :- y = A cos ( t / p - qx ) , where unit of t is s , and unit of x is m. then which is the correct option, I. unit of x and q are equal. ii. unit of x and p are equal. iii. unit of t and q are equal. iv. unit of t and p are equal.

* NEED EXPLANATION *

Answer 1

Basically, according to me.

(iv) is correct.

Because :
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Two things can only be subtracted when they have same units.

Hence,

t/p = qx

=> t= pqx

=> t/x = pq

So, unit of pq is s/m.

Now, Let p = s and q = 1/m (by hit and trial method )

Then,

t/p - qx

=> s/s - 1/m × m

=> 1- 1
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It has same unit .

So , t and p has same units.

****HOPE YOU UNDERSTAND ****

THANK YOU

Answer 2

explanation : expression is y = Acos(t/P - qx), where unit of x is m and unit of t is sec. if we write cosФ, here Ф is angle means dimensionless quantity. hence, option (iv) is correct choice.