Home
Class 12
PHYSICS
Two rods are joined between fixed suppor...

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the length of individual rods with the increase of temperature will be
`"(" alpha_(1), alpha_(2)=` linear expansion coefficient
`A_(1), A_(2)=` Area of rods
`Y_(1), Y_(2)=` Young modulus `")"`

A

`(A_(1))/(A_(2))=(a_(1)Y_(1))/(a_(2)Y_(2))`

B

`(A_(1))/(A_(2))=(L_(1)a_(1)Y_(1))/(L_(2)a_(2)Y_(1))`

C

`(A_(1))/(A_(2))=(L_(2)a_(2)Y_(2))/(L_(1)a_(1)Y_(1))`

D

`(A_(1))/(A_(2))=(a_(2)Y_(2))/(a_(1)Y_(1))`

Text Solution

Verified by Experts

Since tension is the two rods will be same, hence `A_(1)Y_(1)alphaDeltatheta=A_(2)Y_(2)alpha_(2)Deltatheta`
`rArr A_(1)Y_(1)alpha_(1)=A_(2)Y_(2)alpha_(2)`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise PHYSICS PART (A)|32 Videos

  • TEST PAPERS

    BANSAL|Exercise PHYSICS PART (B)|3 Videos

  • TEST PAPERS

    BANSAL|Exercise PHYSICS PART- C|4 Videos

  • SEMICONDUCTORS

    BANSAL|Exercise CBSE Question|32 Videos

Similar Questions

Explore conceptually related problems

The variation of lengths of two moles rods A and B with change in temperature is shown in figure . The ratio of (alpha_(a))/(alpha_(B)) is :-

Two rods AB and BC of equal cross-sectional area are joined together and clamped between two fixed supports as shown in the figure. For the rod AB and road BC lengths are l_(1) and l_(2) coefficient of linear expansion are alpha_(1) and alpha_(2) , young's modulus are Y_(1) and Y_(2) , densities are rho_(1) and rho_(2) respectively. Now the temperature of the compound rod is increased by theta . Assume of that there is no significant change in the lengths of rod due to heating. then the time taken by transverse wave pulse to travel from end A to other end C of the compound rod is directly proportional to

Two metal rods are fixed end to end between two rigid supports as shown in figure. Each rod is of length l and area of cross-section is A . When the systeam is heated up,datermine the condition when the juncation between rods does not shift ? ( Y_(1) and Y_(2) are Young's modulus of materials of rods, alpha_(1) and alpha_(2) are coefficients of linear expansion)

Two metal rods are fixed end to end between two rigid supports, as shown in figure. Each rod is of length 'l' and area of cross-section is A. When the system is heated up, determine the conditioin whenthe juction between rods does not shift. [Given, Y_(1) and Y_(2) are Young's modulus of materials of the rods, alpha_(1) and alpha_(2) are coefficient at linear expansion.

Two rods of different materials having coefficient of thermal expansion alpha_(1), alpha_(2) and young's modulii Y_(1) ,Y_(2) respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If alpha_(1) :alpha_(2)=2 : 3 , the thermal stresses developed in the two rods are equal provided Y_(1) : Y_(2) is equal to

Two rods of equal cross sections, one of copper and the other of steel, are joined to form a composite rod of length 2.0 m at 20^@C , the length of the copper rod is 0.5 m. When the temperature is raised to 120^@C , the length of composite rod increases to 2.002m. If the composite rod is fixed between two rigid walls and thus not allowed to expand, it is found that the lengths of the component rods also do not change with increase in temperature. Calculate Young's moulus of steel. (The coefficient of linear expansion of copper, alpha_c=1.6xx10^(-5@)C and Young's modulus of copper is 1.3xx10^(13)N//m^(2) ).

The coefficient of linear expansion of a rod is alpha and its length is L. The increase in temperature required to increase its legnth by 1% is

BANSAL-TEST PAPERS-PHYSICS
  1. A 100 kg piston encloses 32 g of oxygen gas at a temperature of 27^(@)...

    Text Solution

    |

  2. Two balls of masses 1 kg each are connected by an inextensible massles...

    Text Solution

    |

  3. Two rods are joined between fixed supports as shown in the figure. Con...

    Text Solution

    |

  4. Power radiated by a black body is P0 and the wavelength corresponding ...

    Text Solution

    |

  5. A particle of mass m is subjected to a force vecF=F(0)[cos (t)hati+sin...

    Text Solution

    |

  6. Pressure verus Volume graphs for two process for ideal gas is shown in...

    Text Solution

    |

  7. Consider the adjacent figure. The cube shaped 0.46 carrage ABCDEFGH of...

    Text Solution

    |

  8. A car is acclerating down on an inclined plane as shown in the figure ...

    Text Solution

    |

  9. In travelling transverse wave in string for a small element

    Text Solution

    |

  10. A substance of mass M kg requires a power input of P wants to remain i...

    Text Solution

    |

  11. A particle of mass m kept at the origin is subjected to a froce vecF=(...

    Text Solution

    |

  12. A uniform rod of mass m and length l is rotating with constant angular...

    Text Solution

    |

  13. A heat engine works between a source and a sink maintaned at constant ...

    Text Solution

    |

  14. When the load on a wire is increasing slowly from 2kg to 4kg, the elon...

    Text Solution

    |

  15. Three large sides blocks are kept stationary over one another as shown...

    Text Solution

    |

  16. Statement-1: Experimental results indicate that the molar specific hea...

    Text Solution

    |

  17. lA fixed wedge ABC is an the shape of an equilateral triangle of side ...

    Text Solution

    |

  18. A car is moving uniformly along a circle orf raidus 25Csqrt(3) meter w...

    Text Solution

    |

  19. nA small block is given a velocity v along the inclined palne in the ...

    Text Solution

    |

  20. A uniform semi circular ring of radius R and mass m is free to oscilla...

    Text Solution

    |