3find out V (volume) by integration ... its simple..
its just
1/3pi b^3 [bh/(b-a)] - 1/3 pi a^3[-h + bh/(b-a)]
Ques 1) Find out the net downward thrust on the curved surface of a bucket full of water of height h and radii a and b.
Ques 2) A small uniform tube is bent into a circle of radius r whose plane is vertical. Equal volumes of two fluids whose densities x and y (x > y) fill half the circle. Find the angle that the radius passing thru the interface makes with the vertical.
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5 Answers
3Q1 ....
draw fbd ...
normal force frm ground upward is =ro*g*h*pi a^2 .....(1)
but net downward force = V ro g ..(2)
(2) - (1) = force on curved surface area ..
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@ iiti'mcoming, we don't require integration to find out that volumne.
Completing the cone, we can find the actual ht. of the cone.
Here x=\frac{ab}{b-a}.
Thus volumne is \frac{\pi h (b^2+ab+a^2)}{3}.
So the ans should be \boxed{\frac{\rho g h (b^2+ab+a^2)}{3b^2}}.
