Water from a tap emerges vertically downwards with an initial velocity `V_(0)`. Assume pressure is constant throughout the stream of water and the flow is steady. Find the distance form the tap at which cross-sectional area of stream is half of the cross-sectional area of stream at the tap.

Options

A. ` V_0^2// 2 g `
B. ` 3V_0^2//2g `
C. `2V_0^2//g `
D. ` 5 V_0^2//2g `

Answer

B

Explanation

` AV_0 = A//2 xx V_1 rArr V_1 = 2 V_0 , P + (1)/(2) rho v_1 ^ 2 = P+ rho gh + (1)/(2) rho v_0 ^ 2 `
` rArr v_1^2 = v_0 ^2 + 2 gh 4 v_0 ^ 2 = v _ 0 ^ 2 + 2 gh , h = (3 v _ 0 ^ 2 )/( 2 g )`