Units and Measurement
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Question : 14
Total: 33
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 2 π t ∕ T
(b)y = a s i n v t
(c)y = ( a ∕ T ) sin t ∕ a
Rule out the wrong formulas on dimensional grounds.
(a)
(b)
(c)
(d)y = ( a √ 2 ) ( sin 2 π t ∕ T + cos 2 π t ∕ T )
(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:
The argument of a trigonometrical function, i.e. angle isdimensionless. Now using the principle of homogeneity of dimensions.
(a)
=
= 1 ,
(b) v t = [ L T − 1 ] [ T ] = [ L ] ,
(c)
=
= [ L − 1 T 3 ] ,
(d)
=
= 1 ,
Hence (b) and (c) are wrong on dimensional grounds.
(a)
(b)
(c)
(d)
Hence (b) and (c) are wrong on dimensional grounds.
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