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katteri
03-15-2005, 02:25 PM
One of my friend was recently asked this question by an interviewer and he failed to reply...Thou i found the answer with bit difficulty, for this i wud like to add Geetham members to look in other approaches?
Also if possible let us generate some knowledge base so that it wud help others..

Question 1:
There are two spheres one is hollow and other is solid. Both have equal mass and equal radii..How will u find which sphere is solid?
Answer:
Condition they are not same material, bcos if they are of same material it violates equal mass and equal radii statement.

mass= volume*density

so both their density will be equal.

but the distribution of mass is not equal so they will have different moment of inertia.
When u put a sphere on an inclined plane i.e rolling should happen.
The sphere which takes less time to reach the ground level is solid. (large moment of inertia)

Bluelotus
03-16-2005, 01:30 AM
hollow and solid/dense should give to different types of sound when you percuss the spheres

:think:

vasan
03-16-2005, 02:17 AM
Captain,

Noo.. nooo..

density of the spheres are the same, but the density of the materials will be different. (density of material of hollow sphere is simply the mass/(vol of big sphere-small sphere) )

Easiest way is to test it out like Blue suggested. Bang them both together. The volume is louder in the hollow sphere.

Another, easy to measure way would be to rotate it. Put the ball on a frictionless table, and try rotating it. (Oiled table or a hollow of a decent ball bearing is good). Which ever needs a higher force to rotate will be the hollow sphere.

Moment of inertia is like mass for rotation. To rotate a body (or accelerate its angular rotation) you need to supply some torque (or force via a radial arm). More the moment of inertia more the force. Moment of inertia for hollow sphere is 2/3 (Mr2), and solid sphere is 2/5 (Mr2). So, hollow sphere would need more force to rotate.

But rotating them down an inclined plane will not give you the solution. It will have the same amount of time. That acceleration is pretty much dependent on its weight (and to a small extent on rolling friction).

http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.inertia.html
http://scienceworld.wolfram.com/physics/MomentofInertia.html

Vasan

Priyanka
03-16-2005, 03:24 AM
Which ever needs a higher force to rotate will be the hollow sphere.

Is it so? I thought solid sphere only will need higher force!

What is meant by 'torque' and 'inertia'. Ithellaam eppavoo padicchathu. Marandhuducchu. :oops: Ennai maadhiri tubelight-kalukkum puriyaraa maadhiri explain pannunga paa please! :pray:

vasan
03-16-2005, 03:31 AM
What is meant by 'torque' and 'inertia'. Ithellaam eppavoo padicchathu. Marandhuducchu. Ennai maadhiri tubelight-kalukkum puriyaraa maadhiri explain pannunga paa please!

Inertia is the resistance to motion. higher the weight (mass) higher the inertia !

Torque is rotational force. Force*(distance at which the force is applied) would give you moment. When its applied on a rotating body would give you torque.


Is it so? I thought solid sphere only will need higher force!

to acclerate it or move it (not rotation, just moving it from point a to point b, or translational displacement!), the resistance is inertia (which is directly the mass). Higher the mass, larger the force required to move (or accelerate).

For rotating it, or accelarating its rotation, the inertia is the moment of inertia. Higher the moment of inertia, higher the force (or more properly torque) needed to rotate.

Sari.. solli thanthathukku 10 cents, fees kaatunga first.. :wink: Illainaa naanga ellam eppo Zillionaires aagarathu.. :P

v-

coolian
03-16-2005, 03:44 AM
10 cents? You're gonna kill the market man!

Priyanka
03-16-2005, 03:52 AM
Sari.. solli thanthathukku 10 cents, fees kaatunga first.. Illainaa naanga ellam eppo Zillionaires aagarathu..

Kudukka maatten. Yeenna Vasan solli tharrathu ellaame vilaimathippillaathathu. :P I mean precious. :P Athukku verum 10 cents eppadi kudukkarathu? :Ksp: Onnu pandren. Ungalukku suda suda coffee pottu tharen. Here you go! :P

http://www.nada.kth.se/~snilsson/public/resources/coffee.jpg

ashokcsn_2000
03-16-2005, 04:38 AM
The easiest way is to test the sound emerging from the two... the hollow one will produce a hollow tone while the solid one will have a very damped sound... as the old saying goes ... only empty vessels make more noise... ;)


harder to find out using the moment etc... though they will have different moments bcaus of the mass distribution....

Shy
03-16-2005, 04:39 AM
Vasan --> "aachum aachum aachum......... "

Paavam vasankku cold pudichuduchu... :ahha:

Just kidding ;)

Shy

rsivaraman
03-16-2005, 06:28 AM
I think if you put both of them in water the one that is hollow will float. :think: :think:
-Siva

vasan
03-16-2005, 06:32 AM
I think if you put both of them in water the one that is hollow will float.
-Siva

Nope. Both will sink (if the density of the material is larger than water). It does not matter whether one is hollow or solid.

Vasan

Narayana
03-16-2005, 02:12 PM
Captain.. can you tell for what job interview such a qn. was asked? Computer Engg. padichundu physics ellaam happily forgotten. Ippidi yethavathu ketta tholanjuthu. I think the traditional answer is rolling down the plane...
--N

katteri
03-16-2005, 02:27 PM
Actually my friend is working to a consultant...The guy who runs the consultancy conduct interviews.
He asked my friend this qn.

katteri
03-16-2005, 02:37 PM
Vasan,
Density I meant is material density.

Unless we have a sound measuring instrument we cant find the hollow sphere.

Next vasan, if the force difference is high we can use ur approach. if the force difference between the two sphere is less we cant use.

Another solution:
Put both the spheres in a pot and rotate the pot sufficient enough to make the spheres to rotate(pot can be hold in two hands ). The hollow sphere has high moment of inertia and will settle down soon.

silican
03-16-2005, 02:49 PM
Actually my friend is working to a consultant...The guy who runs the consultancy conduct interviews.
He asked my friend this qn.

:00: :00: :00: Probablly one Buththisaali Consultant. :) These days I get really mad when some consultancy guy with no knowledge about a particular technology calls up and asks questions from a book. :doh:

Adhuvum sila Gult consultants :doh: :doh: Phone eduththu Hello sonna vodane "meeku Project kaavala ?? Websphere Structs Thelusa"nnu adhiradiya erangidaraanga :?

- Silix

PS: Sorry for the side track.

anainar
03-16-2005, 03:17 PM
Given that the mass is the same and so is the volume, with one being hollow, the hollow one will have higher density.

Sound is the one way of identifying which one is hollow, as hollow one will produce higher frequency sound.

The other option which has an inherent assumption is to rotate the spheres with the same force. The hollow one will take longer to settle down, while the solid one will settle down soon. Rolling down the inclined plane also achieves the same thing to some extent, because the spheres start rotating because of rolling friction which ensures constant force as it is a function of friction coefficient and weight. with that same rolling force, hollow sphere will be rotating further while the solid sphere will settle down soon.

Cheers

PS: Easier option, get the CAD model in CATIA V5 or Solidworks or UG NX. Then one can measure the mass moment of intertia and tell you which one is hollow. :D :D :D :D

Cheeers

ns80
03-16-2005, 06:42 PM
I think the easiest, unsophisticated is to tell from the sound when you strike it. namma oorla thengai hollow'a irukka'nu solra adhe principle dhaan :D.


Easier option, get the CAD model in CATIA V5 or Solidworks or UG NX. Then one can measure the mass moment of intertia and tell you which one is hollow.

anainar...enga mela irukkura kovathula ippadi "bad words"a pottu thittirukkeengale :cry:.

rsivaraman
03-16-2005, 06:47 PM
Adhuvum sila Gult consultants Phone eduththu Hello sonna vodane "meeku Project kaavala ?? Websphere Structs Thelusa"nnu adhiradiya erangidaraanga
:lol: :lol: :lol: :lol: :lol:
-Siva

vasan
03-16-2005, 09:18 PM
PS: Easier option, get the CAD model in CATIA V5 or Solidworks or UG NX. Then one can measure the mass moment of intertia and tell you which one is hollow. :D :D

Helloooo..> :00: :00:

Kelvi kettaa enna sales pitch-la irangidureenga.. :P :P (pirated version kidaicha use pannalaam.. :wink:)..


Another solution:
Put both the spheres in a pot and rotate the pot sufficient enough to make the spheres to rotate(pot can be hold in two hands ). The hollow sphere has high moment of inertia and will settle down soon.


The other option which has an inherent assumption is to rotate the spheres with the same force. The hollow one will take longer to settle down , while the solid one will settle down soon. Rolling down the inclined plane also achieves the same thing to some extent, because the spheres start rotating because of rolling friction which ensures constant force as it is a function of friction coefficient and weight. with that same rolling force, hollow sphere will be rotating further while the solid sphere will settle down soon.

Cheers

Katteri,

Anainar sonnathu thaan correct. Hollow sphere would take longer to settle down.

Vasan