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Write names of four dimensionless quantities. If y = A sin(wt - kx) then find out dimension of w/k.
The dimensionless quantities are Coefficient of static friction(μs) coefficient of kinetic friction(μk) Decibels(dB) Poissons ratio Stokes number for Sin X , X should be dimensionless here wt-kx should be dimensionless , so dimension of w/k is equal to dimension of x/t which is m/sec or LT-1
The dimensionless quantities are
Coefficient of static friction(μs)
coefficient of kinetic friction(μk)
Decibels(dB)
Poissons ratio
Stokes number
for Sin X , X should be dimensionless
here wt-kx should be dimensionless , so dimension of w/k is equal to dimension of x/t which is m/sec or LT-1
since the argument of any trignometric quantity have to be neccessarily a radian hence it implies dimention of wt-kx has to be the dimention of radian that is dimentionless.hence dimention of w is T-1and dimention of k is L-1 hence dimention of w/k is L1T -1.
Hi There are infinitely many dimensionless quantities and they are often called numbers. very few of them has been listed below:
Hi
There are infinitely many dimensionless quantities and they are often called numbers. very few of them has been listed below:
y = A sin (wt-kx) According to dimensional analysis , in any term sin ø, ø should be dimensionless Hence, the term wt-kx is also dimensionless where t= time (sec) x= distance (m)
for the term to be dimensionless, wt has no units units of w = s^(-1) k = m^(-1)
Now, units of w/k = m/s
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