Dimensional methods provide three major advantage in verification, derivation and to change the system of units. Any emperical formula that is derived based on this method has to be verified and proportionality constants found by experimental means. The presence or absence of certain factors (numerical constants of 1, 2, π etc) cannot be identified by this method. So every dimensionally correct relation cannot be taken as perfectly correct.
(i) Energy (E) of a oscillating particle is dependent on mass M, frequency 'f' and amplitude 'A' of oscillation. Then energy 'E' is proportional to–
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Ans.
(i)
Sol.E ∝ M a f b A c ML
2 T –2 ∝ M a (T –1 ) b (L) c a = 1, b = 2, c = 2
(ii)
Sol. g = [LT
–2 ] ; m = [M], k = [ML 2 T –2 ]
v = [LT –1 ]
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