A cylinder of height 20m is completely filled with water. The velocity of effux of water `(in ms^(-1))` through a small hole on the side wall of the cylinder near its bottom is

Options

A. 10
B. `20 `
C. `25.5 `
D. `5 `

Answer

B

Explanation

Let ` p _ 0 ` is the atmospheric pressure, ` rho ` is the density of liquid and v the velocity at which water is coming out. Applying the Bernoulli's theorem, just inside and outside the hole,
` p _ ( "inside") = rho gh + 0 = p _ ( "outside" ) + ( pv ^2 ) / ( 2 ) `
` rArr p _ 0 + rho gh = p _ 0 + ( rho v ^ 2 ) /( 2 ) `
` rArr v = sqrt ( 2gh ) `
` rArr v = sqrt ( 2xx 10 xx 20 ) = 20 ms ^( -1 ) `