JEE Class main Answered
solve
Asked by sarveshvibrantacademy | 06 Apr, 2019, 03:00: PM
Expert Answer
Let y be the distance measured from top of the rope towards bottom as shown in figure.
Tension T(y) at a point y of a rope is given by, T(y) = Mg(L-y)/L .............................. (1)
where M is mass of rope and L is length of rope.
Veleocity of transverse wave, v(y) = .........................(2)
where μ is linear mass density i.e. mass per unit length.
let at time τ, the freely falling object meets the pulse at location y = l
then we have for freely falling object, (1/2)gτ2 = l or ......................(3)
Time τ required for the pulse to reach the location y = l is obtained from eqn.(2) as follows
................................(4)
integrating both sides of eqn.(4), we get, .......................(5)
By equating eqn.(3) and eqn.(5), and solving for l in terms of full length of rope L, we get l = (8/9)L
( user can verify the algebra, it is so long and difficult to enter all the steps involved )
hence from bottom, the pulse and the freely falling object meets at a distance (1/9)L
Answered by Thiyagarajan K | 07 Apr, 2019, 10:23: AM
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