Water is filled in a rectangular tank of size `3mxx2mxx1m`. a) Find the total force exerted by the water on the bottom surface of the tank. b) Consider a vertical side of area `2mxx1m`. Take a horizontal strip of wide `deltax` metre in this side, situated at a depth of x metre from the surface of water.Find the force by the water on this strip. c) Find the torque of the force calculate in part b) about the bottom edge of this side. d) Find the total force by the water on this side. e) Find the total torque by the water on the side about the bottom edge. neglect the atmospheric pressure and take `=10ms^-2`.

Answer

A, B, C, D

Explanation

Given `h=1m, A=3xx2=6m^2`
`p=10^3kg/m^3,g=10ms^2`
a. `f=Ahrhog`
`=(3xx2xx1)x10^3xx10`
`=6xx10^4=60000N`
b. The force exerted by water on the strip of width `deltax` as shown
`df=pxxA=(xrhog)xxA`
`=(X)xx10^3x10xx2xdeltax`
`=20000xxdeltaxN`
`c. Inside the liquid force act in every direction due to adhesion
`dt=Fxxr`
`=20000xxdeltax(1-x)N`
d. The total force by the water on that side is given by
`F=int_0^120000 xdeltax`
`rarr F=20000[x^2/2]_0^1`
`=10000N`

e. the torque by the water on that side will be
`=tau=20000xxint_0^Ix deltax(1-x0`
`=20000[x^2/2-x^3/3]_0^1`
`=20000xx[1/2-1/3]`
`=20000/6mN=10000/3mN`