Choose the option showing the correct relation between Poisson’s ratio (σ), Bulk modulus (B) and modulus of rigidity (G).
\(\sigma=\frac{3B-2G}{2G+6B}\)
\(\sigma=\frac{6B+2G}{3B-2G}\)
\(\sigma=\frac{9BG}{3B+G}\)
\(B=\frac{3\sigma-3G}{6\sigma+2G}\)
The Correct Option is A
Solution and Explanation
E = 2G(1 + σ) ….(1)
E = 3B(1 – 2σ) ….(2)
\(1=\frac{2G}{3G}(\frac{1+\sigma}{1-2\sigma})\)
⇒ 3B – 6Bσ = 2G + 2Gσ
⇒ 3B – 2G = σ (2G + 6B)
\(\sigma=(\frac{3B-2G}{2G+6B})\)
So, the correct answer is (A) : \(\sigma=\frac{3B-2G}{2G+6B}\)
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Concepts Used:
Elastic and Inelastic Collisions
Elastic Collision:
According to elastic collision, the kinetic energy of the system will remain constant which means there will be no change in the kinetic energy of the system before and after the collision. It also goes along with the conservation of momentum.
Examples of Elastic Collision
- While playing billiards, balls hit each other.
- A ball is thrown and is bounced to the same height it was thrown from, is an example of elastic collision as there is no net change in the kinetic energy.
- The collision of atoms is also an elastic collision.
Inelastic Collision:
According to inelastic collision, the kinetic energy of the system is not conserved, unlike inelastic collision. The kinetic energy is lost as it gets debauched in other forms of energy like heat, sound, etc, or is absorbed by the body. But they go after the conservation of momentum, like an elastic collision.
Examples of Inelastic Collision
- When the ball is dropped on the ground, it fails to reach the height it was dropped from.
- The accident of two vehicles is an inelastic collision.
- If the clay is thrown at a wall, it sticks to it.
Read More: Elastic and Inelastic Collision
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