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A rope hangs from a rigid support A pulse is set by jiggling the bottom end we want to design a rope in which velocity v of pulse is independent of z the distance of the pulse from fixed end of the rope if the rope is very long the desired function for mass per unit length `mu(z)` in terms of `mu_(0)` (mass per unit length of the top (z=0) g v and z is: A. `mu(z)=mu_(0)e^(-[g//v^(2)]z`B. `mu(z)=mu_(0)e^(+[g//v^(2)]z`C. `mu(z)=mu_(0)log_(e)(g/v^(2))z`D. `mu(z)=mu_(0)e+(v^(2)/g)z` |
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Answer» Correct Answer - A `SigmaF_(z)=0` `(T+dT)+mugdz-T=0` `dT=-mugdz` `also T=muv^(2)` `dT=dmuv^(2)+2vdv dmu` as v is independent of z `dv=0` `dT=v^(2)dmu` from equation (1) and (2) we get `mu int(dmu)/(mu)=-g/v^(2) underset(0)overset(z) intdz` or `mu=mu_(0)e^-(g//v^(2))z` |
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