Elasticity Test - 7

Since work done is converted into heat. Maximum amount of heat produced in the wire is 10 J

We know that

Young Modulus for a perfectly rigid body is infinity, and not zero, so that statement is wrong.

Permanent elongation is caused for perfectly plastic material.

Work done on the wire to strain will be stored as energy which is converted to heat therefore the temperature increases.

Hint: Young's modulus is the property of the material of the wire.

Step 1: Find the change in length of the wire.

We know that with an increase in temperature, the length of a wire changes as; L_t = L_o(1 + αΔT)

where ΔT is the change in the temperature, L₀ is the original length, αα is the coefficient of linear expansion and L_t is the length at temperature T.

Now, we can write, ΔL = L_t − L_o = L_oαΔT

Step 2: Find Young's modulus.

Hint: The elongation of a material depends on its elastic properties.

Step 1: Find the comparative change in the shape of the rods.

A mass M is attached at the centre. As the mass is attached to both the rods, both rods will be elongated. Due to the different elastic properties of the material, rubber changes shape also.

For an ideal liquid, bulk modulus is infinite and shear modulus is zero.

stress = A/F​

As each wire is of same diameter, hence the area of cross section is same for both the wires. As both the wires have the same force (F) and same area of cross-section therefore, stress is same for both the wires

As young's modulus, Y = stress / strain ​or Strain = stress​ / Y

As Y is different for both the wires and stress is same for both the wires, therefore strains is different for both the wires.

If the bridge is used for a long time, due to alternate cycles of stress and strain, the bridge gradually loses its elastic properties and finally reaches a condition called elastic fatigue.