Home
Class 12
MATHS
A certain radioactive material is known ...

A certain radioactive material is known to decay at a rate proportional to the amount present. Initially there is 50 kg of the material present and after 2h it is observed that the material has lost 10 percent of its original mass. Based on these data answer the following questions.
The time at which the material has decayed to one half of its initial mass is

A

`50^(-0.5" ln "9)`

B

`50e^(-2" ln "9)`

C

`50e^(-2" ln "0.9)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We require N at t=4. Substituting t=4 into (3) and then solving for N, we find
`N=50e^(2" ln "0.9)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Matrix Match Type|3 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise (Numerical)|15 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

A mixture consists of two radioactive materials A_1 and A_2 with half lives of 20s and 10s respectively . Intially the mixture has 40g of A_1 and 160 g of A_2 . The amount of the two in the mixture will become equal after:

A small block of superdennse material has a mass of 3xx10^24 kg. It is situated at a height h (much smaller than the earth's radius) from where it falls on the earth's surface. Find its speed when its height from the earth's surface has reduced to h/2 . The mass of the earth is 6xx10^24kg

Two different unknown masses A and B collide. A is initially at rest when B has a speed v. After collision B has a speed v/2 and moves at right angles to its original direction of motion. Find the direction in which A moves after collision.

CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Comprehension)
  1. For certain curves y= f(x) satisfying [d^2y]/[dx^2]= 6x-4, f(x) has l...

    Text Solution

    |

  2. For certain curve y=f(x) satisfying (d^(2)y)/(dx^(2))=6x-4, f(x) has l...

    Text Solution

    |

  3. The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is k...

    Text Solution

    |

  4. The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is ...

    Text Solution

    |

  5. The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is ...

    Text Solution

    |

  6. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  7. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  8. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  9. A curve 'C' with negative slope through the point(0,1) lies in the I Q...

    Text Solution

    |

  10. A curve 'C' with negative slope through the point(0,1) lies in the I Q...

    Text Solution

    |

  11. A curve 'C' with negative slope through the point(0,1) lies in the I Q...

    Text Solution

    |

  12. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int(0)...

    Text Solution

    |

  13. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  14. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  15. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  16. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  17. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  18. Consider a tank which initially holds V(0) liter of brine that contain...

    Text Solution

    |

  19. A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine so...

    Text Solution

    |

  20. A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine so...

    Text Solution

    |