JEE Main20199 Jan 2019Morning ShiftPhysicsMechanical Properties of SolidsActual
A rod, of length L at room temperature and uniform area of cross section A , is made of a metal having coefficient of linear expansion α / ° C It is observed that an external compressive force F is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by ∆ T K Young's modulus, Y for this metal is:
Options
- AF A α ∆ T - 273
- B2 F A α ∆ T
- CF A α ∆ T
- DF 2 A α ∆ T
Correct answer
C. F A α ∆ T
Step-by-step solution
Since the length of the rod does not change, the increment due to increase in temperature will be balanced by the compression due to applied force. Y = F A Δ l l     ⇒   Δ l l = F A Y Also Δ l l = α Δ T ∴     F A Y = α   Δ T Y = F A α Δ T