Home
Class 11
PHYSICS
On the wall of a cylindrical water tank,...

On the wall of a cylindrical water tank, two holes are made as shown in figure. Water coming out from these holes hits the ground at the same point. What will be the ration `h_(1)/h_(2)?`

Text Solution

Verified by Experts

h=total height of water column in tank
`v_(1)`= Velocity of efflux at A
`v_(2)`= Velocity of efflux at B
`v_(2)=sqrt(2g (h-h_(1))`
`v_(1)=sqrt(2gh_(2))`
`t_(1)`= time taken by water to fall from A to R.
`t_(1)=sqrt((2h_(1))/(g))`
Similar `t_(2)`= time taken by water stream to fall from B to R. `t_(2)=sqrt(2(h-h_(2))/(g))`
As the water streams are striking at the same point on the ground.
Therefore, horizontal distance covered by streams coming from A and B are same.
Let `R_(1) and R_(2)` are horizontal ranges.
`R_(1)=R_(2)`
`v_(1) t_(1)=v_(2)t_(2)`,
Putting values we get
`sqrt(2g(h-h_(1)) sqrt((2h_(1))/(g))=sqrt((2gh_(2)) (2(h-h_(2))/(g))`
`(h-h_(1)) h_(1)=h_(2) (h-h_(2))`
`h h_(1)-h_(1)^(2)=h h_(2)-h_(2)^(2)`
`hh_(1)-h_(1)^(2)-hh_(2)+h_(2)^(2)=0`
`h(h_(1)-h_(2))+h_(2)^(2)-h_(1)^(2)=0`
`h(h_(1)-h_(2)) +(h_(2)-h_(1)) (h_(2)+h_(1))=0`
`h(h_(1)-h_(2)) -(h_(1)-h_(2)) (h_(1)+h_(2))=0`
`(h_(1)-h_(2)) (h-(h_(1)+h_(2)) =0`
Case (i) `h_(1)-h_(2)=0 or h_(1)=h_(2)`
Case (ii) `(h-(h_(1)+h_(2))=0 or h_(1)+h_(2)=h`
But `h_(1)+h_(2) ne h`
Case (ii) is not possible
We can say, from case (i) that `h_(1)=h_(2)`
Therefore, the ratio is `(h_(1))/(h_(2))=1`
Promotional Banner

Topper's Solved these Questions

  • MECHANICAL PROPERTIES OF FLUIDS

    MODERN PUBLICATION|Exercise NCERT (Textbook Exercises)|20 Videos

  • MECHANICAL PROPERTIES OF FLUIDS

    MODERN PUBLICATION|Exercise NCERT (Additional Exercises)|11 Videos

  • MECHANICAL PROPERTIES OF FLUIDS

    MODERN PUBLICATION|Exercise Conceptual Questions|29 Videos

  • MATHEMATICAL TOOLS

    MODERN PUBLICATION|Exercise PRACTICE PROBLEMS (10)|12 Videos

  • MOTION IN A PLANE

    MODERN PUBLICATION|Exercise Chapter Practice Test|15 Videos

Similar Questions

Explore conceptually related problems

In a cylindrical water tank there are two small holes Q and P on the wall at a depth of h_(1) from the upper level of water and at a height of h_(2) 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 h_(1) and h_(2) is

figure shows two holes in a wide tank containing a liquid common. The water streams coming out of these holes strike the ground at the same point. The heigth of liquid column in the tank is

A water tank placed on the floor has two small holes, pinched in the vertical wall, one above the other. The holes are 3.3 cm and 4.7cm above the floor. If the jets of water issuing out from the holes hit the floor at the same point on the floor, then the height of water in the tank is

A water tank standing on the floor has two small holes punched in the vertical wall one above the other. The holes are 2.4 cm and 7.6 cm above the floor. If the jest of water from the holes hit the floor at the same point, then the height of water in the tank is

Assertion : To empty an oil tank, two holes are made. Reason : Oil will come out two holes so it will emptied faster.

An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel, was shown in te figure. The water which comes out from the hole at the instant when hole is at height H above the ground strikes the ground at a distance of x from P. Which of the followin is correct for the situation described? (a). The value of x is 2sqrt((2hH)/(3)) (b). The value of x is sqrt((4hH)/(3)) (c). The value ofx can't be computed from information providec. (d). The question is irrevalent as no water comes out from the hole.

A tank is filled to a height H. The range of water coming out of a hole which is a depth H//4 from the surface of water level is

There are two holes O_(1) and O_(2) in a tank of height H. The water emerging from O_(1) and O_(2) strikes the ground at the same points as shows in fig. Then: