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 wt (b) y = a sin vt

$left parenthesis straight c right parenthesis space space space space straight y equals space straight a over straight T sin open parentheses straight t over straight a close parentheses$ $left parenthesis straight d right parenthesis space space space space straight y space equals space fraction numerator straight a over denominator square root of 2 end fraction left parenthesis sin space wt space plus space cos space wt right parenthesis$

(a = maximum displacement of the particle, v = speed of the particle, T = time-period of motion).

Rule out the wrong formulas on dimensional grounds.

Solution

(a) The formula is dimensionally correct.

(b) The formula is wrong, because ‘vt’ has the dimensions of length, according to the gven equation.

(d) The formula is dimensionally correct.

Some More Questions From Units and Measurement Chapter

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