Home
Class 12
MATHS
Water is drained from a vertical cylindr...

Water is drained from a vertical cylindrical tank by opening a value 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 proprortionality `kgt0` depends on the acceliration due to gravity and the geomety of the hole. If is measured in minutes and `k=(1)/(15)` then the time of drain the tank, If the water is 4 m deep to start with is

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Water is leaking from a conical funnel at the rate of 5 cm^3/sec. If the radius of the base of the funnel is 5 cm and the altitude is 10 cm, find the rate at which the water level is dropping when it is 2.5 cm from the top.

Water is leaking from a conical funnel at the rate of 5cm^3//sec . If the radius of the base of funnel is 10 cm and its height is 20 cm, find the rate at which the water level is dropping when it is 5 cm from the top.

In root hair, water enters due to

A tank can contain 384 litres of water. The length of the tank is 3 times of its depth and the breadth is 2 times of its depth. Find the depth of the tank.

A drop of oil rises within water with an upward acceleration of alphag . If alpha is a constant and g is the acceleration due to gravity, find the specific gravity of the oil. Neglect the friction of water.

The base of a water tank is a square of side 3 ft. find the rate of flow of water in the tank, if the water-level at the rate of 1 fr/min.

A drop of oil rises through water with an acceleration alphag . If alpha is a constant quantity and g is the acceleration due to gravity, find the specific gravity of the oil. Neglect the friction of water.

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of

Water is coming out of a hole made in the wall of a freshwater tank. If the size of the hole is increased Will the velocity of efflux of water change?

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. The differential equation (dy)/(dx)=(sqrt(1-y^2))/y determines a f...

    Text Solution

    |

  2. Spherical rain drop evaporates at a rate proportional to its surface...

    Text Solution

    |

  3. Water is drained from a vertical cylindrical tank by opening a value a...

    Text Solution

    |

  4. The population of a country increases at a rate proportional to the...

    Text Solution

    |

  5. An object falling from rest in air is subject not only to the gravit...

    Text Solution

    |

  6. The solution of differential equation x^2=1 +(x/y)^(-1)(dy)/(dx)+((x...

    Text Solution

    |

  7. The solution of the differential equation y^(prime)y^(primeprimeprime)...

    Text Solution

    |

  8. Number of values of m in N for which y=e^(m x) is a solution of th...

    Text Solution

    |

  9. A curve passing through (2,3) and satisfying the differential equation...

    Text Solution

    |

  10. The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 ...

    Text Solution

    |

  11. The solution of the differential equations: (x+x^(3)/(3!)+x^(5)/(5!)...

    Text Solution

    |

  12. A and B are two separate reservoirs of water. Capacity of reservoir...

    Text Solution

    |

  13. If inta^x ty(t)dt=x^2+y(x), then find y(x)

    Text Solution

    |

  14. Given a function ' g' which has a derivative g' (x) for every real x a...

    Text Solution

    |

  15. Solve ((dy)/(dx))^2-x(dy)/(dx)+y=0

    Text Solution

    |

  16. If y+d/(dx)(x y)=x(sinx+logx), find y(x).

    Text Solution

    |

  17. Solve : {xcos(y/x)+ysin(y/x)}ydx={ysin(y/x)-xcos(y/x)}xdy

    Text Solution

    |

  18. Solve xy(dy)/(dx)=x^2+2y^2

    Text Solution

    |

  19. Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

    Text Solution

    |

  20. For the differential equation whose solution is (x-h)^2+(y-k)^2=a^2 (a...

    Text Solution

    |