A heavy but uniform rope of length L is suspended from a ceiling.A particle is dropped from ceiling.At the same instant,the bottom end is given a jerk.Find velocity of wave pulse at an instant when particle and pulse are at same level

For this write the eqn of tension T in rope as function of x(length of string from bottom) to be T=(M/L)gx and µ=M/L so, v of jerk =(T/µ)1/2=(gx)1/2

integrate and then  xjerk=¼gt2 and for particle L-x=½gt2 .So, we get;

t= (4/3L/g)1/2 .So from bottom the jerk will meet particle at L/3

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