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Maths & Physics Collection

Maths & Physics Collection

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[β‰₯Adv] Interesting and high-level (mostly) questions and theory will be posted. Solutions will most often not be posted unless they're elegant (You may ask for one). DM/Comment if there are any errors. Join @ChemGalore for chemistry questions!

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Parabolic Bridge
Parabolic Bridge

f(x) = (x+1)/|x| is NOT Differentiable at
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INJSO 2011
INJSO 2011

Try :)
Try :)

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Guys please fwd in your circle , try to help in any possible way , mahakal will bless all of you .
Guys please fwd in your circle , try to help in any possible way , mahakal will bless all of you .

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Comment with methods
Comment with methods

Extension
Extension

A vertical cylindrical vessel of radius R partially filled with liquid rotates with the liquid around its axis. A balloon of radius r is tied to the side wall of the vessel on a thread of length l; during rotation the thread forms an angle Ξ± with the wall. Determine the angular velocity of rotation of the vessel. MIGHT LOOK SIMILAR, but it is actually a nice problem, judge difficulty in comments.

A vertical cylindrical vessel of radius R partially filled with liquid rotates with the liquid around its axis. A balloon of radius r is tied to the side wall of the vessel on a thread of length l; during rotation the thread forms an angle Ξ± with the wall. Determine the angular velocity of rotation of the vessel. VERY UNIQUE PROBLEM, MIGHT LOOK SIMILAR, but it is actually a nice problem, judge difficulty in comments.

The bottom face of a regular tetrahedron with edge a, completely immersed in a liquid of density ρ, is at depth h. Determine the force exerted by the liquid on the side edge of the tetrahedron if the atmospheric pressure is P. ** VERY relevant problem