Thermal Stress

Q. 18.The tension in the string connected between the blocks is

Q. A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of –39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm ? Co-efficient of linear expansion of brass = 2.0 × 10¯⁵ K¯¹; Young’s modulus of brass = 0.91 × 10¹¹ Pa.

Q. Three capillaries of length l.l/2, l/3 are connected in series.Their radii are r, r/2, r/3 respectively.Then if stream line flow is to be maintained and the pressure across the first capillary is P then

Q. when a tension F is applied in uniform wire of length l and radius r, the elongation produced is e.when tension 2F is applied, the elongation produced in another uniform wire of length 2l and radius 2r made of same material is

Q. 6.Tension T in the string connecting 10 kg and 5 kg blocks (as shown in the figure) is [g = 10 m/s]

Q. 12.A wire of length L suspended vertically from a rigid support is made to suffer extension "l" in its length by applying force F. Work is

Q. An iron rod of length $1\text{m}$ is fixed between two walls as shown in figure. Find thermal stress and thermal strain developed in the rod if it is heated by $\Delta T={20}^{\circ }C$
(Given: Coefficient of linear expansion of iron is $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$; Young's modulus of iron is $2\times {10}^{11}{\text{N/m}}^2$).

1. $24\times {10}^7{\text{N/m}}^2,48\times {10}^{-5}$
2. $48\times {10}^6{\text{N/m}}^2,32\times {10}^{-4}$
3. $32\times {10}^7{\text{N/m}}^2,48\times {10}^{-4}$
4. $48\times {10}^6{\text{N/m}}^2,24\times {10}^{-5}$

Q. 59 An elastic spring has length l(1) when tension in it is 4 N . Its length is l(2) when tension in it is 5N . What will be its length when tension in it is 9 N.?

Q. There is some change in length when a $33000\text{N}$ tensile force is applied on a steel rod of area of cross section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if steel rod is heated, is: (The modulus of elasticity is $3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $1.1\times {{10}^{-5}}^{\circ }{C}^{-1}$)

1. ${10}^{\circ }C$
2. $1^{\circ }C$
3. ${20}^{\circ }C$
4. ${30}^{\circ }C$

Q. There is some change in length when a $33,000\text{N}$ tensile force is applied on a steel rod of area of cross-section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is -
[Take modulus of elasticity $Y=3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $\alpha =1.1\times {10}^{-5}{/}^{\circ }\text{C}$]

1. ${20}^{\circ }\text{C}$
2. ${15}^{\circ }\text{C}$
3. ${10}^{\circ }\text{C}$
4. $0^{\circ }\text{C}$

Q. 23.Find tension in the string and acce ration

Q. A metal bar of length $1\text{m}$ and area of cross-section $1{\text{mm}}^2$ is clamped between two rigid supports. For the material of rod, its Young's modulus is $Y={10}^{11}{\text{N/m}}^2$ and coefficient of linear expansion is $\alpha =1.8\times {10}^{-5}{}^{\circ }{C}^{-1}$. If the temperature of the rod is decreased by $\Delta T={10}^{\circ }C$, the force exerted by the rod on the supports is

1. $9\text{N}$
2. $6\text{N}$
3. $16\text{N}$
4. $18\text{N}$

Q. A rod of length l and radius r is held between two rigid walls so that it is not allowed to expand. If its temperature is increased , then the force developed in it is proportional to

Q.

Which of the following arrangements of a wire clamped on two walls will cause an additional stress within the wire?

1. A piece of wire clamped between two clamps is heated up
2. A piece of wire clamped between two clamps is cooled down

3. Both (a) and (b)

4. Neither (a) nor (b)

Q.

A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will be

1. zero

2. 76 cm

3. < 76 cm

4. > 76 cm

Q.

A uniform steel wire of cross-sectional area $0.20m{m}^2$ is held fixed by clamping its two ends. Find the extra force exerted by each clamp on the wire if the wire is cooled from ${100}^{\circ }C$ to $0^{\circ }C$. Young's modulus of steel = $2.0\times {10}^{11}N/m^2$. Coefficient of linear expansion of steel = $1.2\times {10}^{-5}{/}^{\circ }C$.

1. 500 N
2. 480 N
3. 4.8 N
4. 48 N

Q. A bar of uniform cross-section and having a length $l$ is hanging from the roof. What will be the elongation in bar due to self weight if $\gamma$ is the specific weight of the bar and $Y$ is the young's modulus of elasticity?

Q.

In the given figure, a rod is free at one end and other and is fixed. When we change the temperature of rod by $\Delta$T, then strain produced in the rod will be

1. $\alpha \Delta T$

2. $\frac{1}{2}\alpha \Delta T$

3. zero
4. information incomplete

Q. A steel rod of length $1\text{m}$ is fixed between two walls. If the rod is heated from ${25}^o\text{C}$ to ${35}^o\text{C}$, the stress developed in the rod is expressed as $x\times {10}^7{\text{N/m}}^2$. Find the value of $x$.
(coefficient of expansion for steel is $2\times {10}^{-5}{/}^{\circ }C$, Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$)

1. $2$
2. $4$
3. $7$
4. $8$

Q. A steel rod of length $5\text{m}$ and diameter $30\text{mm}$ is fixed between two rigid supports. Determine the thermal stress and change in diameter of the rod, when the temperature increases by $50{}^{\circ }\text{C}$. Take Young's modulus of elasticity $\left(Y\right)=2.0\times {10}^6{\text{kg/cm}}^2$, coefficient of thermal expansion $\left(\alpha \right)=12\times {10}^{-6}{/}^{\circ }\text{C}$ and Poisson's ratio $\left(\nu \right)=0.3$.

1. $120{\text{kg/cm}}^2,0.0234\text{mm}$
2. $1200{\text{kg/cm}}^2,0.018\text{mm}$
3. $12000{\text{kg/cm}}^2,0.0054\text{mm}$
4. $1200{\text{kg/cm}}^2,0.0234\text{mm}$

Q. Consider a wire of length l, radius r, breaking stress s and breaking strength b, then what happens to breaking stress and breaking strength if, L (new length) and r (new radius) respectively equal: (i) 2l, r ;(ii) 2l, r/2; (iii) 2l, 2r ;(iv)l, r ;(v)l, r/2 ;(vi)l, 2r ;(vii)l/2, r ;(viii)l/2, r/2 ; (ix) l/2, 2r