Water is drained from a vertical cylin...

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth `y ,` where the constant of proportionality `k >0` depends on the acceleration due to gravity and the geometry of the hole. If `t` is measured in minutes and `k=1/(15),` then the time to drain the tank if the water is 4 m deep to start with is

30 min

45 min

60 min

80 min

Text Solution

Verified by Experts

Topper's Solved these Questions

DIFFERENTIAL EQUATION
ARIHANT MATHS|Exercise Solved Examples|1 Videos
DIFFERENTIAL EQUATION
ARIHANT MATHS|Exercise Subjective Type Question|1 Videos
DETERMINANTS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
DIFFERENTIATION
ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

How does value of acceleration due to gravity vary with depth

Show that velocity of escape is proportional to the square root of the product of acceleration due to gravity and the diameter of earth.

Derive an expression for the variation of acceleration due to gravity with depth.

Name the process in which water drops ooze out from margin of leaves.

A spherical ball of salt is dissovlging water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface. Prove that the radis is decreasing at a constant rate.

Show that for same change in acceleration due to gravity, the depth to which a body is to be taken is twice the height?

Find the cost of preparing a closed cylindrical tank of height 2.8 m and base diameter 4 m at the rate of Rs 100 per sq. m.

ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)

Water is drained from a vertical cylindrical tank by opening a valve...
Text Solution
|
If f:R-{-1}toR and f is differentiable function satisfies: f((x)+f(y...
Text Solution
|
A solution curve of the differential equation (x^2+xy+4x+2y+4)((dy)/(d...
Text Solution
|
Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(...
Text Solution
|
Let y(x) be a solution of the differential equation (1+e^(x))y^(')+ye^...
Text Solution
|
Let y(x) be a solution of the differential equation (1+e^(x))y'+ye^(x)...
Text Solution
|
Solve the differential equation : y sqrt(1-x^2)dy-sqrt(1+y^2)dx=0
Text Solution
|
Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...
Text Solution
|
A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...
Text Solution
|
Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...
Text Solution
|
Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...
Text Solution
|
Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...
Text Solution
|
Consider the statements : P : There exists some x IR such that f(x)...
Text Solution
|
Differentiate the following w.r.t x (log x)^(cos x)
Text Solution
|
Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...
Text Solution
|
Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...
Text Solution
|
Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...
Text Solution
|
If a curve y=f(x) passes through the point (1,-1) and satisfies the di...
Text Solution
|
Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...
Text Solution
|
Let the population of rabbits surviving at a time t be governed by t...
Text Solution
|
At present, a firm is manufacturing 2000 items. It is estimated tha...
Text Solution
|