Question

For a perfectly rigid body
A. Young’s modulus is infinite and bulk modulus is zero.
B. Young’s modulus is zero and bulk modulus is infinite.
C. Young’s modulus is infinite and bulk modulus is also infinite.
D. Young’s modulus is zero and bulk modulus is also zero.

Answer 1

Hint: The above problem can be resolved using the mathematical relation of the young's modulus, which is given by taking the fraction of the stress-induced within the body, due to applied load and change in the dimension produced due to the corresponding magnitude of stress. Moreover, the rigid body is much tough to respond to any such change in dimension.


Complete step by step solution
The mathematical relation for the young’s modulus of for a rigid body is given as,
$$Y={\displaystyle \frac{\sigma }{\epsilon }}$$
Here, $$\sigma$$ denotes the stress within the rigid body and $$\epsilon$$ is the magnitude of strain produced.
For a rigid body, the value for the strain is zero. In other words, the rigid body does not produce elongation for any given amount of load.
Then the young’s modulus is,
 $$\begin{array}{l}Y={\displaystyle \frac{\sigma }{\epsilon }}\\ Y={\displaystyle \frac{\sigma }{0}}\\ Y=\mathrm{\infty }\end{array}$$
The bulk modulus is in direct relation with the young’s modulus. Hence, Bulk modulus for the rigid body is also infinite.
 Therefore, for a perfectly rigid body, the young’s modulus is infinite and bulk modulus is also infinite and option (A) is correct.


Note: To resolve the given problem, one must be familiar with the generalised formula of young's modulus of elasticity along with the significance of stress and strain in the formula. The stress resembles the application of load in the context of the area of any object and strain accounts for the deviation in length, observed due to applied load. The rigid bodies are the good resistors to the strains, and their values of Young's modulus and Bulk modulus are related directly to each other.