Think Infinite
If the acceleration of topmost block is k g , find k .
The answer is 2.
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1 solution
Please explain your third line i.e T a 1 + 2 T a 2 + 4 T a 3 = . . . . = 0 ???
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That's something called the Virtual Work Method .
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You have posted a note i think .
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@Chirayu Bhardwaj – Yup, I had. I did not much from the note, but I reshared some problems whose solutions contained virtual work method.
Will you please explain it.
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@A Former Brilliant Member – I'm on tab, so I can't type LaTeX. But I'll surely take the opportunity to help you. Please view the solution to the following question.
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@Swapnil Das – The solution is of finite pulley system and I did it the same way Satvik Pandey has done but it didn't help me in this question How can we solve questions involving infinite pulley system
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@A Former Brilliant Member – I think the solution is enough for understanding. Where are you getting stuck?
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@Swapnil Das – I can't understand why T a 1 + 2 T a 2 + . . . . . is zero
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@A Former Brilliant Member – 1)For the topmost block, the forces acting are
Mg downwards and Tension T upwards...also it is moving with acceleration a1. a1=(T/m) - g
2) For the second block, the forces acting are
Mg downwards and Tension T/2 upwards...moving with acceleration a2. a2=(T/2m) - g ... ... ... This process continues infinitely... (I.e. Tension for third block is T/4, fourth block is T/8.......)
That's why the terms T/2, T/4, T/8... in the expression...
In pulley system, the sum of the product of acceleration and their respective tension is zero.....
Putting those values in the expression and solving with the help of infinite G.P., we get a1= g/2
Hope, this explanation is much clearer than what I had posted before..
@A Former Brilliant Member – That's virtual work for an infinite number of strings!
The "Rao IIT Academy" Symbol !!! This problem came in one of the recent Rao tests and I presume the problem's picked up from there!
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You're probably right. Therefore, the solution isn't original :P
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Actually, even I had written the test.
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@Miraj Shah – Yeah, I took It from the tests only... This question has a flavour of both Maths and physics..and interesting too.. That's why posted it..:)
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@Ganesh Iyer – Ya..its a good question!
@Ganesh Iyer – This question was famously posted by David Morin, in his perhaps, weekly physics challenges. Nice to relive the moment.