23. Which of the following relation cannot be deduced using dimensional analysis?
[The symbols have their usual meanings]
(1) y = A sin(ot + kx)
(2) v = u + at
(3) k = mv
(4) All of these
Answers
Answer:
None of the relations given in the options can be deduced using dimensional analysis.
Hence the correct answer is (d) all of these.
According to the rule, the method of dimensions can not be used to derive relations other than product of power function
Example:
s=ut +1/2 a t^2 can not be derived by this method
answer : option (4) all of these.
explanation : it is already mentioned, The symbol have their usual meanings .
A is amplitude , w is angular frequency [by mistake you wrote o] , k is wave number and y is displacement of particle. we cannot deduced this relation by dimensional because in dimensional analysis sin(wt + kx) is always taken as dimensionless.
now in second option , v + u + at
it also cannot deduced by dimensional analysis because dimensions cannot be used to derive relations other than product of power function.
similarly, option (c) k = mv , k is kinetic energy, m is mass and v is velocity . we can apply here dimensional analysis but as we know, kinetic energy, k = 1/2 mv²
given relation is wrong . so, it also cannot deduced by dimensional analysis.
hence, option (4) is correct.