Questions
The frequency (f) of a stretched string depends upon the tension F (dimensions of force), length l of the string and the mass per unit length of string. Derive the formula for frequency.
detailed solution
Correct option is A
Suppose, that the frequency f depends on the tension raised to the power a, length raised to power b and mass per unit length raised to power c. Then,f∝Falbμc or, f=kFalbμcHere, k is a dimensionless constant. Thus, [f]=[F]a[η]b[μ]c or, M0 L0 T-1=MLT-2a[ L]bML-1c or, M0 L0 T-1=Ma+c La+b-c T-2aFor dimensional balance, the dimensions on both sides should be same.Thus, a+c=0… (ii) a+b-c=0...(iii) and -2a=-1… (iv) Solving these three equations, we geta=12, c=-12 and b=-1Substituting these values in Eq. (i), we getf=k(F)1/2(l)-1(μ)-1/2 or, f=klFμExperimentally, the value of k is found to be 12Hence,f=12lFμTalk to our academic expert!
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The quantities A and B are related by the relation A/B = m, where m is the linear mass density and A is the force, the dimensions of B will be
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