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#Mechanics

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Let $m$ be the mass of the ring so $2m$ is the mass of each loop.Now by symmetry its clear that the ring moves downwards so let its acceleration be $a$ then each of the loops moves with acceleration $w$ .But consider a loop+ring.Both must have a common acceleration along the common normal (here radius).So $w/√2=a/√2$ so $w=a$ .The normal reaction between them be $N$ and friction be $f$ then we have $(N/√2-f)/2m=R\alpha =f/2m$ .so $f=N/2√2$ , $a=w=N/4√2m$ .For the ring $mg-√2N=ma$ .Yields $N=4√2mg/9$ .So normal given by ground if $F=2mg+Ncosπ/4=22mg/9$ .And accn of the ring $a=g/9$ .Friction is $f=2mg/9=2/9$ .Note that we don't take into account the radial acceleration since $t=0$ there is nt any given to the system.

Spandan Senapati - 4 years, 1 month ago

There is going to be torque by friction about the centre of the ring right?

Sumanth R Hegde - 4 years ago

I have included that.If the friction you are taking about is due to ground then I have included it.And if it's friction between both ring and hoop then the problem says to neglect that.

Spandan Senapati - 4 years ago

@Spandan Senapati – Yes. I read ur comment wrong ... I read radial acceleration as angular acceleration

Sumanth R Hegde - 4 years ago

@Sumanth R Hegde – Ok... Give your best in jee adv.....All the best....

Spandan Senapati - 4 years ago

@Spandan Senapati – Thx! I hope things go right as well

Sumanth R Hegde - 4 years ago

$A,D$ are correct.simple mechanics q.

Spandan Senapati - 4 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$