Question

In a cylindrical water tank there are two small holes Q and P on the wall at a depth of h₁ form upper level of water and at a height of h₂ from the lower end of the tank respectively as shown in the figure. Water coming out from both the holes strike the ground at the same point. The ratio of h₁ and h₂ is:

• A. 1
• B. 2
• C. >1
• D. <1

Answer 1

Answer: (A)

1

Answer 2

The two streams strike at the same point on the ground,

⇒ R₁ = R₂ = R

⇒ v₁ t₁ = v₂ t₂ …(1)

where v₁ = velocity of efflux at 1 =$\sqrt { 2 \mathrm { gh } _ { 1 } }$ and v₂ = velocity

of the efflux at 2

= t₁ = Time of fall of the water stream through

(1) =

t₂ = Time of fall of the water stream through (2) =

Putting these values in equation (1), we obtain,

(H – h₁) h₁ = (H – h₂) h₂ ⇒ [H-(h₁ + h₂)] [h₁ – h₂] = 0

⇒ H = h₁ + h₂ is irrelevant because the holes are at two

different heights, there fore h₁ = h₂ ⇒ (h₁/h₂) = 1

Therefore (1).