Find the relation between h and R so that average force on the side walls of a cylinder becomes equal to the force at the bottom.

Asked by Amyra B | 20th Nov, 2014, 06:22: PM

Expert Answer:

Let h be height of cylinder, ρ be the density of water, R is the radius of cylinder.
The pressure inside the cylinder due to liquid is not same. The point at geater depth feels greater pressure and hence greater thrust.
Therefore average pressure on vertical walls of a cylinder,
Pav=begin mathsize 14px style fraction numerator 0 plus hρg over denominator 2 end fraction equals 1 half hρg end style
begin mathsize 14px style Thrust space on space the space walls space of space clynder equals straight P subscript av cross times straight A equals 1 half hρg cross times 2 πhR equals πh squared ρgR......... left parenthesis straight i right parenthesis left parenthesis where space straight A space is space area space of space cylinder equals 2 πhR right parenthesis In space bottom space pressure space due space to space liquid space is space uniform space at space all space point comma straight P equals hρg Therefore space thrust space on space bottom equals straight p cross times straight A subscript straight b equals πR squared hρg......... left parenthesis ii right parenthesis left parenthesis where space straight A subscript straight b space is space area space at space base space of space cylinder equals πR squared right parenthesis From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis πh squared ρgR equals πR squared hρg rightwards double arrow straight R equals straight h Hence space proved. end style

Answered by Priyanka Kumbhar | 21st Nov, 2014, 11:25: AM