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If the kinetic energy of pulse travelling in a taut string is Kxx10^(-2) mJ then find the value of K (Given T=10 N & mu=0.1 kg//m

Answer»


Solution :at given time `y=m_(1)X 0 LT x lt 0.1` m
`=m_(2)x+C 0.1 m lt x lt 0.15` m
`m_(1)=10^(-3)/0.1 = 10^(-2) (V_(omega)=sqrt(T/mu))`
`m_(2)=10^(-3)/0.05=2xx10^(-2)`
`dK=1/2dmV_(p)^(2)=1/2mu dx(-V_(omega)(dely)/(delx))^(2)`
`intdK=1/2muV_(omega)^(2)[m_(1)^(2) underset0overset(0.1)intdx+m_(2)^(2) underset(0.1)overset(0.15)intdx]`
`K=1/2T[m_(1)^(2)(0.1)+m_(2)^(2)(0.5)]`
`K=1/2T[10^(-4)(0.1)+4xx10^(-4)(0.5)]`
`=10/2[10^(-4)](0.3)=0.15mJ`


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