Question

If x longitudinal strain is produced in a wire of Young's modulus y, then energy stored in the material of the wire per unit volume is [MP PMT 1987, 89, 92; CPMT 1997; Pb. PMT 1999; KCET 2000; AIIMS 2001]
A) y{{x}^{2}} B) 2\,y{{x}^{2}} C) \frac{1}{2}{{y}^{2}}x D) \frac{1}{2}y{{x}^{2}}

Answer 1

Energy stored per unit volume is given by
E = 1/2 × strain × stress -------(1)
Here E is energy per unit volume .

∵ Young's modulus , Y = stress/strain
so, strain = stress/Y , put it in above equation (1)

E = 1/2 × stress/Y × stress
= stress²/2Y

Given, Stress = x and Young's modulus, Y = y
Then, E = x²/2y

Hence, option (D) is correct

Answer 2

Correct option: (D) (1/2) yx2 Explanation: Energy stored per unit volume = 1/2 × stress × strain = 1/2 × 4 × strain × strain ----- Y = [{stress} / {strain}] = 1/2 yx2