A tank, which is open at the top, contains a liquid up to a height H.

1.	A tank, which is open at the top, contains a liquid up to a height H. A small hole is made in the side of the tank at a distance y below the liquid surface. The liquid emerging from the hole lands at a distance x from the tank.(a) If y is increased from zero to H, x will first increase and then decrease.(b) x is maximum for y = H/2. (c) The maximum value of x is H. (d) The maximum value of x will depend on the density of the liquid.
Answer» Correct Answer is: (a, b, & c) The velocity of efflux = v = √2gy. The emerging liquid moves as a projectile and reaches the ground in time t, where, H - y = 1/2 gt² or t =√(2(H - y))/g ∴ x = vt= 2 √(H - y)y. For x to be maximum,dx/dy = 0 or y = H/2 ∴ x_max = H.

A tank, which is open at the top, contains a liquid up to a height H. A small hole is made in the side of the tank at a distance y below the liquid surface. The liquid emerging from the hole lands at a distance x from the tank.(a) If y is increased from zero to H, x will first increase and then decrease.(b) x is maximum for y = H/2. (c) The maximum value of x is H. (d) The maximum value of x will depend on the density of the liquid.

Answer»

Correct Answer is: (a, b, & c)

The velocity of efflux = v = √2gy.

The emerging liquid moves as a projectile and reaches the ground in time t, where,

H - y = 1/2 gt² or t =√(2(H - y))/g

∴ x = vt= 2 √(H - y)y.

For x to be maximum,dx/dy = 0 or y = H/2

∴ x_max = H.