The adjacent graph shows the extension of a wire of length 1 m suspended from the top of a roof

Q: The adjacent graph shows the extension (Δl) of a wire of length 1 m suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is 10-6m2, Calculate from the graph the young’s modulus of the of the material of the wire

Numerical

(a)2 × 1011N/m2

(b) 2× 10-11N/m2

(c) 3× 1012N/m2

(d) 2× 1013N/m2

Ans: (a)

Two rods of different material having coefficients of thermal expansion α1 , α2 and young’s moduli Y1, Y2 respectively…

Q: Two rods of different material having coefficients of thermal expansion α1 , α2 and young’s moduli Y1 , Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If α1 : α2 = 2:3, the thermal stresses developed in the two roads are equal provided Y1 : Y2 is equal to

(a) 2:3

(b) 1:1

(c)3:2

(d) 4:9

Ans:(c)

Sol: Thermal Stress $\large \sigma = Y \alpha \Delta \theta $

$\large \sigma_1 = \sigma_2 $

$\large Y_1 \alpha_1 \Delta \theta = Y_2 \alpha_2 \Delta \theta $

$\large \frac{Y_1}{Y_2} = \frac{\alpha_2}{\alpha_1}= \frac{3}{2}$

The following four wires are made of the same material. Which of these will have the largest extension…

Q: The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

(a)Length=50cm, diameter=0.5mm

(b) Length=100cm, diameter=1mm

(c) Length=200cm, diameter=2mm

(d) Length=300cm, diameter=3mm

Ans: (a)

Sol: $\large \Delta L = \frac{F L}{A Y}$

$\large \Delta L = \frac{F L}{(\frac{\pi D^2}{4}) Y}$

$\large \Delta L \propto \frac{L}{D^2}$