Home
Class 12
MATHS
A spherical ball of salt is dissolving i...

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

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Level -1|102 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Level -2|69 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2cm.

Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2cm.

The rate constant of any reaction is proportional to the concentration of the reactants.

A spherical balloon is being inflated so that its volume increase uniformaly at the rate of 40 cm^(3)//"minute" . The rate of increase in its surface area when the radius is 8 cm, is

Suppose that water is emptied from a spherical tank of radius 10 cm. If the depth of the water in the tank is 4 cm and is decreasing at the rate of 2 cm/sec, then the radius of the top surface of water is decreasing at the rate of

The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
  1. A spherical ball of salt is dissolving in water in such a manner that ...

    Text Solution

    |

  2. Let f,g : [-1,2] to be continuous functions which are twice different...

    Text Solution

    |

  3. Let f:Rrarr(0,oo)andg:RrarrR be twice differentiable functions such th...

    Text Solution

    |

  4. If f:R is a differentiable fucntion such that f(x) gt 2f(x) for all x...

    Text Solution

    |

  5. The point(s) on the curve y^3+\ 3x^2=12 y where the tangent is ver...

    Text Solution

    |

  6. On the ellipse 4x^2+9y^2=1, the points at which the tangents are paral...

    Text Solution

    |

  7. If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >...

    Text Solution

    |

  8. If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=...

    Text Solution

    |

  9. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  10. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  11. If f(x)=xe^(x(1-x)), then f'(x) is

    Text Solution

    |

  12. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

  13. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

    Text Solution

    |

  14. The function f(x)=(log (pi+x))/(log (e+x))," is "

    Text Solution

    |

  15. Let fa n dg be increasing and decreasing functions, respectively, from...

    Text Solution

    |

  16. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

    Text Solution

    |

  17. Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h ...

    Text Solution

    |

  18. Let f(X) be a polynomila of degree four having extreme values at x =1 ...

    Text Solution

    |

  19. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  20. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  21. The total number of local maxima and local minima of the function f...

    Text Solution

    |