In the given figure a string of linear mass density `3xx10^(-2)` kg//m and length `L=1` m, is stretched by a froce `F=(3-kt)N`, where k is a constant and t is time in sec. At the time `t=0`, a pulse is generated at the end P of the string Find the value of k (in N//s) if the value of force becomes zero as the pulse reaches point Q.

Answer

`20`

Explanation

Time taken by pulse to reach from P to `Q (t_(0))=F_(0)/k` where `F_(0)=3`
Now, `V=sqrt(T/m)Rightarrow(dX)/(dt)=sqrt((F_(0)-kt)/m)`
`:.underset0oversetLint dX=1/sqrt(m) underset0overset0int(F_(0)-kt)^(1//2)dt`
`L=2/3ksqrt(m) F_(0)^(3//2)`
`:.k=2/(3L) sqrt(F_(0)^(3)/m)=2/(3xx1)sqrt((3xx3xx3)/(3xx10^(-2)))=(2xx3)/(3xx0.1)=20`