# Why should the bulk modulus of a perfectly rigid body be infinite?

Also, what can we say about the Young's modulus and Shear Modulus of a perfectly rigid body and why?

• Can you please tell me what do you understand by a rigid body? – Knight Dec 4 '19 at 14:08
• A rigid body cannot change its shape and distribution of mass. I do not know any formal definition sadly. – aditya_stack Dec 4 '19 at 14:10
• Try a reading of Wikipedia article on rigid body (just first few lines). – Knight Dec 4 '19 at 14:12
• Well the bulk modulus is just $$E_v = \frac{stress}{strain}$$ and as you have said that distance between two points doesn’t change that means strain is zero and anything divided by zero is infinite. Therefore bulk modulus is infinite. – Knight Dec 4 '19 at 14:18
• "The distance between any two given points on a rigid body remains constant in time regardless of external forces exerted on it." Okay this line answers the question, and there is also a semi-formal derivation given by @VK_fan. Thanks. – aditya_stack Dec 4 '19 at 14:18

Bulk modulus is defined as $$B=-V\frac{P}{\Delta V}$$ It is obvious that we can't change the volume of an ideal rigid body so $$\Delta V$$ tends to zero hence magnitude of bulk modulus tends to $$\infty$$