on the basis of dimensions, decide which of the following relations for the displacement undergoing simple harmonic motion is not correct:
a. y= a sin 2 nt/T
b. y= a sin vt
c. y= a/T (sin (t/a)
d. y= a2^1/2 (sin nt/T-cos 2nt/T)
Answers
Answered by
2
Answer:
B. y = a sin vt
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Answered by
1
Explanation:
Correct option is
B
y=asinvT
C
y=
T
a
sin(
a
t
)
b.,c.: In option (a) and (d) the dimensions of y and a in L.H.S. and R.H.S. are equal to L and while in option (b) angle is v.t (where v is velocity)
∴ dimension of v.t is [LT
−1
][T]=[L].
So sinvt is not dimensionless so option (b) is wrong. In option (c) in R.H.S. dimension of amplitude
T
a
=
[T]
[L]
=[LT
−1
] which not equal to the dimension of y i.e L and angle
a
t
=
[L]
[T]
=[LT
−1
] is not dimensionless.
Hence, verifies the option (b) and (c).
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