Two identical blocks A and B each of mass M are placed on a long inclined plane (angle of inclination = θ ) with A higher up than B. The coefficients of friction between the plane and the blocks A and B are respectively µ A and µ B with tan θ > µ B > µ A. The two blocks are initially held fixed at a distance d apart. At t = 0 the two blocks are released from rest.

Find the time in which the two blocks collide?

My answer ; - \[\large{t_{Collision} = \sqrt{\dfrac{2d \tan \theta ( \sin \theta - \mu_A \cos\theta)}{g (\sin \theta - \mu_B \cos\theta)}}}\]

What about you?Is my answer correct?

**I am not sure with my answer, please all of us, lets discuss!**

## Comments

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TopNewest@Md Zuhair Yup, my answer matches with the one given by Brian Charlesworth and yes, its correct :-) ! Sorry yours was wrong :-( . – Ayon Ghosh · 4 months ago

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– Md Zuhair · 4 months ago

Ya I got it nowLog in to reply

The two blocks will meet up after a time \(t\) such that

\(d + \dfrac{g}{2}(\sin(\theta) - \mu_{B}\cos(\theta)) = \dfrac{g}{2}(\sin(\theta) - \mu_{A}\cos(\theta))\),

which when solved for \(t\) gives us \(t_{c} = \sqrt{\dfrac{2d}{g\cos(\theta)(\mu_{B} - \mu_{A})}}\).

Suppose \(\mu_{A} = \mu_{B}\). Then you wouldn't expect the two blocks to ever meet, but your formula would have them meeting after \(\sqrt{\dfrac{2d\tan(\theta)}{g}}\) seconds, while mine would have \(t_{C} \to \infty\) as expected. – Brian Charlesworth · 4 months ago

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– Steven Chase · 4 months ago

This seems to be a generalization of that "underkill" problem that was posted recently.Log in to reply

\(\tan(\theta) \gt \mu_{B} \Longrightarrow \theta \gt \arccos\left(\dfrac{1}{\sqrt{1 + \mu_{B}^{2}}}\right)\). – Brian Charlesworth · 4 months ago

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– Steven Chase · 4 months ago

It would be interesting to consider this same problem with a curved surface and friction.Log in to reply

– Md Zuhair · 4 months ago

Okay! So go on, Can you post one?Log in to reply

– Steven Chase · 4 months ago

I'll look into itLog in to reply

– Rohith M.Athreya · 4 months ago

One can generalise further : If the time at which they first meet is \(t_{1} \), the subsequent times of meeting again (after collision) turns out to be odd multiples of \(t_{1} \)Log in to reply

– Md Zuhair · 4 months ago

Hey! Whats your JEE Main score?Log in to reply

– Rohith M.Athreya · 4 months ago

around 290 :(Log in to reply

– Md Zuhair · 4 months ago

Well, lets see your picture in newspaper!Log in to reply

my friends are expecting around 310-315 – Rohith M.Athreya · 4 months ago

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– Md Zuhair · 4 months ago

Okay, leave that! You will surely qualify JEE Advanced with rank above 0.5k this year brother! I have seen your brain!Log in to reply

I'll take your word for it(if i write advanced)

thank you! – Rohith M.Athreya · 4 months ago

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@Rohith M.Athreya are you giving either of ISI or CMI ? – Aditya Narayan Sharma · 4 months ago

SoLog in to reply

II no – Rohith M.Athreya · 4 months ago

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– Md Zuhair · 4 months ago

If you dont write advanced, ill delete my Brilliant account!Log in to reply

– Md Zuhair · 4 months ago

Which underkill problem? Can you please provide the link sir?Log in to reply

– Steven Chase · 4 months ago

https://brilliant.org/problems/mechanics-overkill-2/?ref_id=1349100Log in to reply

– Md Zuhair · 4 months ago

Thank you,Log in to reply

@Md Zuhair From where did you get this problem? – Ankit Kumar Jain · 4 months ago

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– Md Zuhair · 4 months ago

i did a very fine mistake! Its correct now!Log in to reply

– Md Zuhair · 4 months ago

Thanks sir!Log in to reply

Let me tag some of you,

@Aniket Sanghi , @Rohith M.Athreya , @Ayon Ghosh , @Steven Chase , @Brian Charlesworth! – Md Zuhair · 4 months ago

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– Rohith M.Athreya · 4 months ago

http://olympiads.hbcse.tifr.res.in/olympiads/wp-content/uploads/2017/01/INPhO2017-Solution-20170131.pdfLog in to reply