@sammygerbil how do you get 3 in equation of normal

@sammygerbil we are not given coefficient of restitution . So we cannot comment

first line = 2nd question

second line =1st question

Coefficient of restitution is 1. The string is elastic (but very stiff).

Solution for falling chain is explained in the link.

okay I got it second question . Actually the file is not downloading

@sammygerbil so it will rebound

Oh you are thinking of the collision with the ground? No we do not know the COR for that "so we cannot comment".

So there is no solution? Only the answer 1.25m?

yes

I do not understand why mass B is "gently" lifted up to the pulley. Why "gently"?

while lifting up there will be no impulse

Also why is mass B "held" at the position shown? They are the same weight so there is no tendency to move if they are released from the position shown.

While B is lifted up the string is not taut so there is no impulse via the string.

Sorry , I am confused

should I ask in jee preparation rrom

I have asked it there

Yes. It it good to get other views on the problem.

I think the problem is like 2 equal masses m on a frictionless surface, attached by a string, initially loose. I think gravity makes no difference. B is given an impulse mv, when the string becomes taut there is an elastic collision (ie transfer of momentum via the string). B stops, A moves towards B with speed v. They collide again (this time directly), A stops and B moves with speed v. The system continues "bouncing" indefinitely.

So in Q1 I think the masses continue moving (A up, B down) until B hits the ground or A hits the pulley.

1.25 m

@blue What is your solution?

@blue $v=\sqrt {2g}$

ohh

There is no common velocity. Strings behave like springs - they are elastic.

See my answer to physics.stackexchange.com/q/309785 and also the link in my answer which makes reference to published articles in Applied Mathematics. Being elastic is not incompatible with being inextensible.

"Elastic" has (at least) two meanings in physics : (1) extensible, (2) conserving energy (as in collisions).

I am using the latter because there is a "collision" via the string. This collision conserves energy.

Well if that is what you have been taught for the examination, use that. It gives you the answer which the examiner wants. But it is not what happens with real strings.

typo

Are you talking about real strings? Or strings used in the exercises which are given to you?

As I said, inextensible is not incompatible with being "elastic" (ie conserving energy) in the limit of an infinite spring constant.

I'm using the definition appropriate for collision problems, but also for all deformable bodies : an elastic deformation returns all of the work you put in.

does inextensible = elastic

in this question it is inextensible not elastic

No, I don't think it is semantic. Unless you are saying that you have been taught to model strings as completely inelastic, we are disagreeing about how real strings behave.

@sammygerbil we have been taught ideal string = inelastic = inextensible

And in these question we assume the string to be ideal

unless it is specified

@Koolman Yes that is what I thought : we are using different definitions of an "ideal" string. My definition includes conserving energy.

@Koolman What is your difficulty?

not getting answer from this

I am not sure that I want to tackle the whole of this question. Unlike the last two it is unnecessarily complicated. I think you do know all the relevant ideas and formulas. EG en.wikipedia.org/wiki/….

$c=\sqrt {\frac{T}{\mu}}$ or $c=\sqrt {\gamma \frac{P}{\rho}}$

@sammygerbil and in this what is the use that tension is reduced

@Koolman You have enough information to calculate the frequency f of the organ pipe. The frequency of the string is f +/- 5. We don't know if is + or -. When tension in the wire is reduced this lowers its frequency. There are fewer beats, so this makes the frequency of the wire closer to f. This tells you which it is : + or -.

@sammygerbil what is the mistake in my try

I think in second case that is of organ pipe I will use $c=\sqrt {\gamma \frac{P}{\rho}}$

Oh I have taken wrong lambda for f1 @sammygerbil

it would be 2

$f2=(9/10)\sqrt{\rho RT/M}$

as you said f2-f1 =5