Most Important Selected Qs for JEE AdvancedPhysicsMechanical Properties of Solids
A thin copper rod of length is suspended vertically from the ceiling by one of its ends. Density of copper is , Young's modulus is Y and Poisson's ratio is . Then which of the following are correct ?
Options
- AThe strain in the rod due to its own weight is g l 2 Y
- BThe elastic deformation energy stored in the rod due to its own weight is ^2 g^2 l^3 A 6 Y where A is area of
- CVolume strain of the rod is g l 2 Y [1- ]
- DVolume strain of the rod is g l 2 Y [1-2 ]
Correct answer
D. Volume strain of the rod is g l 2 Y [1-2 ]
Step-by-step solution
At, P, T=A x g Elongation of element dx is d e= T(d x) A Y Deformation energy of the element is d U= 1 2 T(d e)= T^2 d x 2 A Y gathered d U= (A x g)^2 d x 2 A Y = A ^2 g^2 x^2 d x 2 Y u= d u= A ^2 g^2 2 y = ₀^ x^2 d x= A ^2 g^2 ^3 6 y gathered