A brass rod of length `1 m` is fixed to a vertical wall at one end, with the other end keeping free to expand. When the temperature of the rod is increased by `120^@C`, the length increases by `3 cm`. What is the strain?
Text Solution
Verified by Experts
After the rod expands to the new length, there are no elastic forces developed internally in it. So strain `=0`
Two rods of different materials and identical cross sectional area, are joined face to face at one end their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by 30^(@)C , the magnitude of the displacement of the joint of the rod is (length of rods l_(1) = l_(2) = 1 unit , ratio of their young's moduli, Y_(1)//Y_(2) = 2 , coefficients of linear expansion are alpha_(1) and alpha_(2) )
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) ).
A rod of length l is released from the vertical position on a smooth horizontal plane. What is the nature of motion of the free end of the rod ?
A rod of length / and radius r is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to
In the given figure, a rod is free at one end and other end is fixed. When we change the temperature of rod by Deltatheta , then strain produced in the rod will be
If rod is initially compressed by Deltal length then what is the strain on the rod when the temperature (a) is increased by Delta theta (b) is decreased by Delta theta
Two rods of equal cross-sections, one of copper and the other of steel are joined to from a composite rod of length 2.0m at 20^(@)C the length of the copper rod is 0.5m . When the tempertuare 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 foundthat the length fo the component rod also do not change with increase in temperature. Calcualte the Young's modulus of steel. Given Young's modulus of copper = 1.3xx10^(11) N//m^(2) the coefficent of linear expansion of copper alpha_(C) = 1.6xx10^(-5)//.^(@)c
A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250^(@)C , if the original lengths are at 40.0^(@)C ? Is there a 'thermal stress' developed at the junction ? The ends of the rod are free to expand. Coefficient of linear expansion of brass = 2.0 xx 10^(-5).^(@)C^(-1) and that of steel =1.2 xx 10^(-5).^(@)C^(-1) .
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 :
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