AP EAMCET202017 Sep 2020Evening ShiftPhysicsMechanical Properties of SolidsActual
Find the stress developed inside a tooth cavity filled with copper when hot tea at temperature of (57^ C ) is drunk. You can take body (tooth) temperature to be (37^ C ) and ( =1.7 10⁻⁵ ^ C ⁻¹ ), bulk modulus for copper (B=140 10^9 Nm ⁻² ).
Options
- A(1.4 10^8 Nm ⁻² )
- B(1.9 10^8 Nm ⁻² )
- C(2.0 10^8 Nm ⁻² )
- D(3.4 10^7 Nm ⁻² )
Correct answer
A. (1.4 10^8 Nm ⁻² )
Step-by-step solution
Temperature of hot tea, (t₂=57^ C ) Normal temperature of tooth, (t₁=37^ C ) ( =1.7 10⁻⁵ C ⁻¹ ) Bulk modulus, (B=140 10^9 Nm ⁻² ) Thermal stress in tooth cavity ( aligned & = Bulk modulus Volumetric strain & =B V V =B t & [ V=V t] & =B 3 t & [ =3 ] & =3 B t=3 B (t₂-t₁ ) & =3 140 10^9 1.7 10⁻⁵(57-37) & =1.4 10^8 Nm ⁻² aligned )