Home
Class 12
PHYSICS
Water is filled to a height in a fixed v...

Water is filled to a height in a fixed vertical cylinder placed on horizontal surface. At time t = 0 a small hole I drilled at a height `h//4` from bottom of cylinder shown. The cross section area of hole is a and the cross-section area of cyliner is A such that `A gt gt a`.

Let the value of horizontal distance of point where the water fall on horizontal surface from bottom of cylinder be x as shown. Then from time t =0 till water comes out of hole, pick the correct statement :

A

`(A)/(a) sqrt((3h)/(2g))`

B

`(a)/(A) sqrt((3h)/(2g))`

C

`(A)/(a) sqrt((2h)/(3g))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
The initial velocity of water coming out of hole is horizontal and hole is at a height `(h)/(4)` from ground. Hence time taken by water to reach ground is `t = sqrt((2(h//4))/(g))` which remains constant
`:. x = vt` where v is velocity of effux…
Since v decreases with time x will decrease

Let y be the height of water surface above hole
`:. -(dy)/(dt)=(av)/(A)=(asqrt(2gy))/(A)`
`:. underset(3h//4)overset(0)(int) (dy)/(sqrt(2gy))= underset(0) overset(t)(int) -(a)/(A) dt`
`:. t = (A)/(a) sqrt((3h)/(2g))`
Promotional Banner

Topper's Solved these Questions

  • DAILY PRACTICE PROBLEM

    RESONANCE ENGLISH|Exercise DPP No.35|20 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE ENGLISH|Exercise DPP No.36|20 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE ENGLISH|Exercise DPP No.33|20 Videos

  • CURRENT ELECTRICITY

    RESONANCE ENGLISH|Exercise High Level Problems (HIP)|19 Videos

  • ELECTRO MAGNETIC WAVES

    RESONANCE ENGLISH|Exercise Exercise 3|27 Videos

Similar Questions

Explore conceptually related problems

Water is filled to height h in a fixed vertical cylinder placed on horizontal surface. At time t = 0 a small hole a drilled at a height h//4 from bottom of cylinder as shown. The cross section area of hole is a and the cross-section area of cylinder is A such that A gtgt a . Let the value of horizontal distance of point where the4 water fall on horizontal surface from bottom of cylinder be x as shown. Then from time t = 0 till water comes out of hole, pick the correct statement:

Water is filled to height h in a fixed vertical cylinder placed on horizontal surface. At time t = 0 a small hole a drilled at a height h//4 from bottom of cylinder as shown. The cross section area of hole is a and the cross-section area of cylinder is A such that A gtgt a . Let the value of horizontal distance of point where the4 water fall on horizontal surface from bottom of cylinder be x as shown. Then from time t = 0 till water comes out of hole, pick the correct statement:

Will the height of the water column change if the cross section of the water column is made wider ?

A cylinider is filled with non viscous liquid of density d to a height h_(0) and a hole is made at a height h_(1) from the bottom of the cylinder. The velocity issuing out of the hole is

A syringe containing water is held horizontally with its nozzle at a height h above the ground as shown in fig the cross sectional areas of the piston and the nozzle are A and a respectively the piston is pushed with a constant speed v. Find the horizontal range R of the stream of water on the ground.

In a capillary tube , water rises to a height of 4 cm If its cross section area were one forth , the water would have to rises a height of

Water is filled in a container upto height 3m. A small hole of area 'a' is punched in the wall of the container at a height 52.5 cm from the bottom. The cross sectional area of the container is A. If a//A=0.1 then v^2 is (where v is the velocity of water coming out of the hole)

A tank if filled with water upto height H. When a hole is made at a distance h below the level of water. What will be the horizontal range of water jet ?

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm, and the other dimensions are as shown. Calculate the total surface area.

If cross- sectional area of limb I is A_(1) and that of limb II is A_(2) then velocity of the liquid in the tube will be, (cross- sectional area of tube is very small)