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A book with many printing errors contai...

A book with many printing errors contains four different forumlae for the displacement y of a particle undergoing a certain periodic motion : (i) `y = a sin (2pi t)/(T)` (ii) `y = a sin upsilon t` (iii)`y = (a)/(T) sin (t)/(a)` (iv)`y= (a)/(sqrt2)[sin(2pi t)/(T) + cos (2pi t)/(T)]` Here, a is maximum displacement of particle, `upsilon` is speed of particle, T is time period of motion. Rule out the wrong forumlae on dimensinal grounds.

A

`y=A sin (2pi t//T)`

B

`y=A sin v t`

C

`y=(A//T) sin (t//A)`

D

`y=(A//sqrt2)(sin omega t+cos omegat)`

Text Solution

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The correct Answer is:
B, C
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Knowledge Check

  • A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion. 1. y= asin""(2pit)/(T) 2. y= asinvt 3. y= (a)/(T)sin""(t)/(a) 4. y= (asqrt(2))(sin((2pit)/(T))+ cos((2pit)/(T))) where a is the maximum displacement of the particle, v is the speed of the particle, T is the time period of motion. Then dimensionally

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    D
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  • The displacement of a particle is given at time t, by: x=A sin (-2 omega t ) + B sin^(2) omega t Then,

    A
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    B
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    D
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