IIT JEE-AIEEE 2012, Entrance Notifications, Study Tips, Engineering Preparation, Practice Test Papers, Experts Advice

Ask iit jee aieee pet cbse icse state board community

Discussion Response Post to: only brains are allowed

Forum Index -> Mechanics -> View Full Question

Author

Message

waterdemon (3810)

Forum Expert

total posts: 1048
Offline

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 !!!!!!!!!!!!!!!!!!!!!!!!!!

Always available for help ! But Remember Don't hesitate to ask a good Question but Be damn serious for Questioning a weak one. <TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0"> <TR><TD> <DIV ALIGN="right">Glitter Graphics</DIV></TD></TR></TABLE> [img]http://www.avatarsdb.com/avatars/fat_man_walk.gif[/img][url=http://www.avatarsdb.com/] [img]http://www.avatarsdb.com/avatars/angry_smile.gif[/img][/url][url=http://www.avatarsdb.com/] [img]http://www.avatarsdb.com/avatars/moon.gif[/img][/url]

Like 0 people liked this

Free Sign Up!

Preparing for IIT-JEE ?

Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor

@ INR 1,995/-

For Quick Info