Question

A block of mass m is suspended from a wire of length L, area of cross section A and Young's modulus Y. The elastic potential energy stored in the wire is

a. ½ M²g²L/AY
b. ½ Mg/ALY
c. ½ M²g²A/YL
d. ½ MgY/AL

Answer 1

The elastic potential energy stored in the wire is calculated using the formula PE = (1/2)L²Y/A. Therefore, the correct option is (c) ½ M²g²A/YL.

Step-by-step explanation:

The elastic potential energy stored in the wire is given by the formula PE = (1/2)AL²Y/A, where AL is the change in length, Y is Young's modulus, and A is the cross-sectional area. In this case, the wire is being used as a simple pendulum, so the change in length AL is equal to L. Therefore, the elastic potential energy stored in the wire is given by PE = (1/2)L²Y/A.

To match this form of the equation, the closest option is (c) ½ M²g²A/YL, which can be rewritten as (1/2)L²Mg²/AY, where M is the mass of the block.

Therefore, option (c) ½ M²g²A/YL is correct.