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Mechanics

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Joined:	11 Jun 2007
Post:	1048

14 Jun 2007 18:53:09 IST

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only brains are allowed

None

here in this question , there is a cube of dimension of a,b,c and there is a door like an arc of a circle having radius R and due to the open space between the door and the cube ther appears a hole which causes the water to leak out of the cube filled fully with water afrom point T .

Now you all have to find the force F that has to be applied on point T to prevent

leakage of water through hole "T" ?

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ASHUTOSH SINGH

New kid on the Block

Joined: 15 Jun 2007

Posts: 29

16 Jun 2007 08:46:30 IST

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WELL I CAN'T GET THE HECK OF IT.

simi singh

New kid on the Block

Joined: 15 Jun 2007

Posts: 8

16 Jun 2007 16:19:12 IST

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i dont think wasting your time on these questions will get u to iit

waterdemon

Forum Expert

Joined: 11 Jun 2007

Posts: 1048

16 Jun 2007 16:35:45 IST

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Helo Jatt punjabi

you aaren't wasting ur time

If u think so then u have already lost the race to Get into IIT

COz such questions help u get ur concepts get better

And are nothing but practice for you However I am putting on the solution I some minutes.

waterdemon

Forum Expert

Joined: 11 Jun 2007

Posts: 1048

16 Jun 2007 19:08:36 IST

Like 4 people liked this

So here is the answer Well it was a difficult one and I tried putting it up for

The GOIITians

Here

= Angle between the line (of R inthe fig. ) and the horizontal '' b ''

First

The pressure that will be acting on the potion aprt from the door will be

dP = P ( a - Rsin

)

As the length of the door will be (a - R Sin

)

dF_x = Pcg(a - R Sin

)R.d

* Sin

dF_y = Pcg (a- Rsin

)Rd

* Cos

Knowing that T = F*R

So the below relations are as per the horizontal and vertical components

And

is the density of the liquid that is inside the Cube.

dT_Fx=

cg ( a -Rin

) d

.Sin

. (R - RCos

)

dT_Fy =

cg (a - Rsin

.Cos

.(RSin

)

Now resolving along the line of resultant "F"

dT = dT_Fx+ dT_Fy

Where T is the torque

cg(a - Rsin

)Rd

.Sin. (R - Rcos

) +

cg(a -Rsin

)Rd

.Cos

.Rsin

cgR² [ (a-Rsin

)Sin

.(1-Cos

+ (a-Rsin

)Cos

.Sin

]

cgR² [ (aSin

- RSin²

)(1 - Cos

+ (aCos

- R.Sin

.cos

)(Sin

cgR² [ aSin

- aSin

.Cos

- RSin²

+ RSin²

.Cos

+ aCos

.Sin

- RCos

.Sin²

] d

cgR²[ aSin

- RSin²

] d

cgR² [ -a [cos

] { from 0 to pi/2 } - R(1 - Cos2

/ 2 ) ] d

cgR² [ a - R ( d

/ 2 - Cos2

/ 2 .d

]

cgR² [a - R

/4 - (Sin2

/4).d

Sin 2

/4 = 0 as it is from 0 to

cgR²[a - R

/4 ]

Therefore we will get

Where F is the force to be applied on point T to avoid leakage of liquid

F*R = T

F*R =

cgR²[a - R

/4]

F =

cgR[a - R

/4]

Hence the answer

plZ rate me for my efforts

Cheers !!!!!!!!!!!!!!!!!!!!!!!!!!

waterdemon

Forum Expert

Joined: 11 Jun 2007

Posts: 1048

16 Jun 2007 19:37:13 IST

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Come on atleast rate me for my efforts yaar !!!!!!!!!!!11

waterdemon

Forum Expert

Joined: 11 Jun 2007

Posts: 1048

16 Jun 2007 23:36:48 IST

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Have a look at this Question it is really good for all the GOIITians .

And plZ rate me.

waterdemon

Forum Expert

Joined: 11 Jun 2007

Posts: 1048

17 Jun 2007 21:24:53 IST

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I cannot understand that why are u all neglecting such a good question

OK don't rate me but plZ this is for ur benefit only.

S k

Blazing goIITian

Joined: 12 May 2007

Posts: 574

17 Jun 2007 21:57:00 IST

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hey man..i do appreciate ur efforts..........BUT

saying that this wud help us is completely wrong ( frm point of view of IIT )

these kind of questions are for those who are aiming for

INTERNATIONAL PHYSICS OLYMPIAD....

moreover....u didnt get the desired response from goiitians because

the question was a bit difficult to understand pictorially....

moreover....ur question shud have that something which forces us all to attempt ur questions...

like i got a pretty awsome response for my killer series ( a series of tough mathematical problems which can be found in the alzebra section..) because each ques. seemed to be solvable yet unsolvable...

newayz...i wud give u a salute for ur efforts...
astalavista...

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