Mechanics.......!!!

A rigid body rolling without slipping strikes an inclined plane of inclination 60° and begins to roll without slipping up the inclined plane. The maximum height attained by the rigid body will be highest for :-

Assume initial velocity of each body of to be same and their radius be in ratio 1:2:3:4 (Solid Cylinder, Solid Sphere, Ring, Hollow Sphere).

Ring Hollow sphere Solid Cylinder Solid sphere

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1 solution

Manish Bhargao
Feb 2, 2015

Can somebody add a nice solution.....I want to see your approach....i did it with radius of gyration logic.....

thnkx...

I ask you to share your that solution. 'Cause you're the Asker, so you might can the solution easiest !

Muhammad Arifur Rahman - 6 years, 4 months ago

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can you please tell me how to upload a image or how to write down in nice latex form.......

by the way I just compared the k^2/R^2 values.....It's understood now...... there are so many people here who can write solution in correct format....so I asked.... :D

manish bhargao - 6 years, 4 months ago

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B y E n e r g y c o n s e r v a t i o n w e c a n w r i t e M g h = 1 2 M V 2 [ 1 + K 2 R 2 ] s o t h e c o n c l u s i o n i s m o r e t h e r a t i o o f K 2 R 2 m o r e i s t h e h e i g h t r e a c h e d . S o , r e m e m b e r i n g t h e r a t i o s o f d i s c a n d a l l s t u f f R i n g i s t h e a n s w e r . . . By\quad Energy\quad conservation\quad we\quad can\quad write\quad Mgh=\frac { 1 }{ 2 } M{ V }^{ 2 }\left[ 1+\frac { { K }^{ 2 } }{ { R }^{ 2 } } \right] \\ so\quad the\quad conclusion\quad is\quad more\quad the\quad ratio\quad of\quad \frac { { K }^{ 2 } }{ { R }^{ 2 } } \quad more\quad is\quad the\quad height\quad reached.\\ So,\quad remembering\quad the\quad ratios\quad of\quad disc\quad and\quad all\quad stuff\\ \\ Ring\quad is\quad the\quad answer...

manish bhargao - 6 years, 4 months ago

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@Manish Bhargao The value for k^2/R^2 is maximum for hollow sphere!! If the radius of ring is 3R and the radius of hollow sphere is 4R, then that value for ring is 9, whereas for hollow sphere is 32/3! Please recheck...

A Former Brilliant Member - 6 years, 4 months ago

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@A Former Brilliant Member Oops.....You are absolutely....correct..!!actually while writing the solution I just didn't mind about the radius ratios.. thnkx....and well done.

manish bhargao - 6 years, 4 months ago

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@Manish Bhargao thanks...:)

A Former Brilliant Member - 6 years, 4 months ago

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@A Former Brilliant Member Are you in XII std

manish bhargao - 6 years, 4 months ago

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@Manish Bhargao ALL the best for JEE....

manish bhargao - 6 years, 4 months ago

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@Manish Bhargao I'm in XI, Wbu?? Good luck to you too!:)

A Former Brilliant Member - 6 years, 4 months ago

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@A Former Brilliant Member Well Iam in XII.Preparing for my boards....how much do you expect in jEE mains.

manish bhargao - 6 years, 4 months ago

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@Manish Bhargao I don't know...Never thought about it. Let's just hope for the best! And good luck for your boards!! and the JEE, as well...:)

A Former Brilliant Member - 6 years, 4 months ago

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@A Former Brilliant Member Thnkx.....

manish bhargao - 6 years, 4 months ago

@Manish Bhargao There you are.

Now its a logical and nice solution. Good!

But you need to specify the Radius of Gyration of each of them and write down the values of K 2 R 2 \frac{K^2}{R^2} of them. Then you should compare them and show that its highest for the Ring.

I know you've done all of these, but there are Learners in our Brilliant. org community.

So you shouldn't be ambiguous to them.

So its better you implement your nice reply in the solution with the following points met.

Undoubtedly its a brilliant problem.

Muhammad Arifur Rahman - 6 years, 4 months ago

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@Muhammad Arifur Rahman Would you plzz illustrate the meaning and use of the radius of gyration... and how actually this prblm ha been slvd with this concept.

I 've not heard of it before ......i jst used my practical knowledge and guessed it to be the answer ...how the radius of gyration helped ????

tanmay goyal - 6 years, 4 months ago

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@Tanmay Goyal Well, if you really wanna learn, why don't you Google it?

Obviously Google will be much more helpful that what I write in this limited, short collaboration.

There's plenty of Wiki's about it. Those will satisfy you nicely.

....Hope it helped...

Muhammad Arifur Rahman - 6 years, 4 months ago

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@Muhammad Arifur Rahman I know that google has an unending stuff on almost all topics as such .... Bt i 've obsrved a difference occurs often when on one side you google it and on the other you learn from someone who has already learned it nicely ... I 've already googledd..it ....but this is not hidden from you too that the differnce arises...

I thought about that and so to accomodate in my learning the understanding of others' of the topic ..I asked you .. There is no problem otherwise...

By the way Thnks for the sugesstion.

tanmay goyal - 6 years, 4 months ago

You copied my problem . If you wanted the solution you could've written it there only.

Abhishek Sharma - 6 years, 3 months ago

Could u tell me that this question is related to which topic or what topic i have to study to answer this question ??

Chirayu Bhardwaj - 5 years, 6 months ago

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This question belongs to the category of rotational mechanics, @Chirayu Bhardwaj

A Former Brilliant Member - 5 years, 6 months ago

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