Select the correct answers in each of the following options:

1. A wire is stretched to double of its length. Its strain is:

(a) 2

(b) 1

(c) 0

(d) 0.5

Solution: We know that

Let length of the wire is L. Since the wire is stretched to double, therefore, change in length is also L. Therefore, Strain = L/L = 1

2. Which of the modulus of elasticity is involved in compressing a rod to decrease its length?

Young’s Modulus

Bulk Modulus

Modulus of elasticity

None of the above

Explanation: Young’s Modulus is the ratio of tensile strain (and tensile strain is one which is produced in the length of the object) and the tensile stress (tensile stress is one which is applied perpendicularly on the object). Unlikely, bulk modulus is involved in the cases when the object is subjected to pressure from all sides, and modulus of elasticity is any modulus involved in the stress to strain ratio.

3. A wire is stretched to double of its length. The strain is

(a) 2

(b) 1

(c) zero

(d) 0.5

4. If both the length and radius of the rod are doubled, then the modulus of elasticity will

(a) Increase

(b) Decrease

(c) Remains same

(d) Doubled

Explanation: Let force F is applied on an object of length L such that the change in its length is Δ x, then

Now according to the conditions of the given problem,

L^’ = 2L and r^’ = 2r. Put in equation 1.

Comparing with equation (1) we see the modulus of elasticity has decreased (by half).

5. Curie temperature is a point where

Diamagnetism changes to paramagnetic

Paramagnetic changes to diamagnetism

Ferromagnetism changes to paramagnetic

Paramagnetic changes to ferromagnetism

6. A cable breaks if stretched by more than 2 mm. It is cut into two equal parts. How much either part can be stretched without breaking?

25 m

1 mm

2 mm

0.5 m

Solution: Strain is the ratio of change in the length to the length of the cable. If L is the length of the cable and 2 mm is the change (deformation) in the cable, then

If the cable is broken in two equal parts, then length of each part is L/2. Let the maximum change is now L^’. Then

(Note: Strain is the property of the material and remains constant for a certain material under the same conditions).