Home
Class 11
PHYSICS
Two metal rods are fixed end to end betw...

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

Text Solution

Verified by Experts

Since, each rod is prevented from expansion so, they are under compression and mechanical strain. The net strain in each rod.
`epsi_(1)=alpha_(1)1DeltaT-(F1)/(AY_(1)),epsi_(2)=alpha_(2)1DeltaT-(F1)/(AY_(2))rArrepsi_(1)=epsi_(2)=0`
`alpha_(1)1DeltaT-(F1)/(AY_(1))=0andalpha_(2)1DeltaT-(F1)/(AY_(2))=0`
`alpha_(1)1DeltaT-(F1)/(AY_(1))=0andalpha_(2)1DeltaT-(F1)/(AY_(2))=0`
Solving, we get `alpha_(1)Y_(1)=alpha_(2)Y_(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Two metal rods of the same length and area of cross-section are fixed end to end between rigid supports. The materials of the rods have Young moduli Y_(1) and Y_(2) , and coefficient of linear expansion alpha_(1) and alpha_(2) . The junction between the rod does not shift and the rods are cooled

Two rods having length l_(1) and l_(2) , made of materials with the linear coefficient of expansion alpha_(1) and alpha_(2) were welded together. The equivalent coefficients of linear expansion for the obtained rod:-

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 ")"

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 ")"

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 ")"

Two rods of equal cross sections area are joined end the end as shown in figure. These are supported between two rigid vertical walls. Initially the rods are unstrained . If temperature of system is increased by DeltaT then junction will not shift if -

A thin rod of negligible mass and area of cross section S is suspended vertically from one end. Length of the rod is L_(0) at T^(@)C . A mass m is attached to the lower end of the rod so that when temperature of the rod is reduced to 0^(@)C its length remains L_(0) Y is the Young’s modulus of the rod and alpha is coefficient of linear expansion of rod. Value of m is :

The coefficient of linear expansion of an in homogeneous rod change linearly from alpha_(1) to alpha_(2) from one end to the other end of the rod. The effective coefficient of linear expansion of rod is

The coefficient of linear expansion of an in homogeneous rod change linearly from alpha_(1) to alpha_(2) from one end to the other end of the rod. The effective coefficient of linear expansion of rod is

Two rods of different materials are placed between massive walls as shown in figure. The cross section of the rods is A, their moduil of elastricity are E_(1) and E_(2) respectively. If rods are heated by t degrees, then (coefficients of liner expansion of material of rods are alpha_(1) and alpha_(2) respectively)