Home
Class 12
PHYSICS
A clock with a metallic pendulum gains 6...

A clock with a metallic pendulum gains `6` seconds each day when the temperature is `20^(@)C` and loses `6` second when the temperature is `40^(@)C`. Find the coefficient of linear expansions of the metal.

A

`1.4xx10^(-5) "^(@)C^(-1)`

B

`1.4xx10^(-6) "^(@)C^(-1)`

C

`1.4xx10^(-4) "^(@)C^(-1)`

D

`1.4xx10^(-6) "^(@)C^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
For simply pendulum `T=2pi`
`sqrt((l)/(g)) implies T alpha l^(1//2) implies (DeltaT)/(T) = (1)/(2) (Deltal)/(l) = (1)/(2) alphaDeltatheta`
Assuming clock gives correct time at temperature
Promotional Banner

Topper's Solved these Questions

  • GEOMETRICAL OPTICS

    ALLEN |Exercise EXERCISE -02|82 Videos

  • GEOMETRICAL OPTICS

    ALLEN |Exercise EXERCISE -03|11 Videos

  • GEOMETRICAL OPTICS

    ALLEN |Exercise SOME WORKED OUT EXAMPLES|84 Videos

  • CURRENT ELECTRICITY

    ALLEN |Exercise EX.II|66 Videos

  • GRAVITATION

    ALLEN |Exercise EXERCISE 4|9 Videos

Similar Questions

Explore conceptually related problems

A pendulum clock loses 12s a day if the temperature is 40^@C and gains 4s a day if the temperature is 20^@C , The temperature at which the clock will show correct time, and the co-efficient of linear expansion (alpha) of the metal of the pendulum shaft are respectively:

A steel tape 1 m long is correctly calibrated for a temperature of 27.0^(@)C . The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0^(@)C . What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is 27.0^(@)C ? Coefficient of linear expansion of steel =1.20xx10^(-5)K^(-1) .

A steel tape Im long is correctly calibrated for a temperature of 27.0 ^(@) C . The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0^(@) C .What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0^(@) C ? Coefficient of linear expansion of steel = 1.20 xx 10^(-5) K^(-1) .

A steel wire of cross section 1 mm2 is heated at 60^(@) C and tied between two ends family. Calculate change in tension when temperature becomes 30^(@) C coefficient of linear expansion for steel is alpha = 1.1 xx 10 ^(-5) "”^(@)C ^(-1), Y =2 xx 10 ^(11) Pa. (Change in length of wire due to change in temperature (Delta t) is Delta l = alpha l Delta t)

A large steel wheel is to be fitted on to a shaft of the same material. At 27 ^(@) C , the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using dry Icel. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: alpha_("steel ") = 1.20 xx 10^(-5) K^(-1) .

A large steel wheel is to be fitted on to a shaft of the same material. At 27^(@)C , the outer diameter of the shaft is 0.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft ? Assume coefficient of linear expansion of the steel to be constant over the required temperature range : alpha_("steel")=1.20xx10^(-5)K^(-1) .

A simple pendulum made of bob of mass m and a metallic wire of negligible mass has time period 2 s at T = 0^(@)C . If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S . If the coefficient of linear expansion of metal is alpha then value of S is :

A wooden wheel of radius R is made of two semicircular part . The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2piR . To fit the ring on the wheel, it is heated so that its temperature rises by DeltaT and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircle parts together. If the coefficient of linear expansion of the metal is alpha , and it Young's modulus is Y, the force that one part of the wheel applies on the other part is :

A clock pendulum made of invar has a period of 2 s at 20^(@)C . If the clock is used in a climate where average temperature is 40^(@)C , what correction (in seconds ) may be necessary at the end of 10 days to the time given by clock? (alpha_("invar") = 7 xx 10^(-7) "^(@)C, 1 "day" = 8.64xx10^(4)s )

An equilateral triangle ABC is formed by two copper rods AB and BC and one is aluminium rod which heated in such a way that temperature of each rod increases by DeltaT. Find change in the angle angleABC. (Coefficient of linear expansion for copper is alpha _(1). and for aluminium is alpha2 .).

ALLEN -GEOMETRICAL OPTICS-EXERCISE -01
  1. The coefficient of linear expansion 'alpha' of a rod of length 2 m var...

    Text Solution

    |

  2. The coefficient of linear expansion 'alpha' of the material of a rod o...

    Text Solution

    |

  3. A clock with a metallic pendulum gains 6 seconds each day when the tem...

    Text Solution

    |

  4. A steel scale measures the length of a copper rod as l(0) when both ar...

    Text Solution

    |

  5. The coefficient of apparent expansion of a liquid when determined usin...

    Text Solution

    |

  6. Three rods of the same dimensions have thermal conductivities 3k , 2k ...

    Text Solution

    |

  7. A cup of tea cools from 80^(@)C to 60^(@)C in one minute. The ambient ...

    Text Solution

    |

  8. Ice starts forming in lake with water at 0^(@)C and when the atmospher...

    Text Solution

    |

  9. There is a small hole in a container. At what temperature should it be...

    Text Solution

    |

  10. A surface at temperature T(0)K receives power P by radiation from a sm...

    Text Solution

    |

  11. Two different rods A and B are kept as shown in figure . The variation...

    Text Solution

    |

  12. The area of cross-section of rod is given by A= A(0) (1+alphax) where ...

    Text Solution

    |

  13. Following graph shows the correct variation in intensity of heat radia...

    Text Solution

    |

  14. A red star and a green star radiate energy at the same rate which star...

    Text Solution

    |

  15. 250 g of water and equal volume of alcohol of mass 200 g are replaced ...

    Text Solution

    |

  16. The weight of a person is 60 kg . If he gets 10 calories of heat throu...

    Text Solution

    |

  17. Two identical masses of 5 kg each fall on a wheel from a height of 10 ...

    Text Solution

    |

  18. Hailstone at 0^@C from a height of 1 km on an insulating surface conve...

    Text Solution

    |

  19. In figure , heat is added to a pure substance in a closed container ra...

    Text Solution

    |

  20. Objects A and B that are initially separated from each other and well ...

    Text Solution

    |