Thermal Expansion
PHXI11:THERMAL PROPERTIES OF MATTER

366798 A rod, of length \(L\) at room temperature and uniform area of cross-section \(A\), is made of a metal having coefficient of linear expansion \(\alpha /^\circ C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \(\Delta TK\). Young's modulus \(Y\), for this metal is

1 \(\frac{{2\;F}}{{\;A\alpha \Delta T}}\)
2 \(\dfrac{F}{A \alpha \Delta T}\)
3 \(\dfrac{F}{2 A \alpha \Delta T}\)
4 \(\frac{F}{{\;A\alpha (\Delta T - 273)}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366799 Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
\(\left(\alpha_{1}, \alpha_{2}=\right.\) linear expansion coefficients \(A_{1}, A_{2}=\) Area of rods \(Y_{1}, Y_{2}=\) Young modulus)
supporting img

1 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{1} Y_{1}}{\alpha_{2} Y_{2}}\)
2 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{1} \alpha_{1} Y_{1}}{L_{2} \alpha_{2} Y_{2}}\)
3 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{2} \alpha_{2} Y_{2}}{L_{1} \alpha_{1} Y_{1}}\)
4 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{2} Y_{2}}{\alpha_{1} Y_{1}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366800 A fine steel wire of length \(4\,m\) is fixed rigidly in a heavy brass frame as shown in figure. It is just taut at \({20^{\circ} {C}}\). Find the tensile stress developed in steel wire if whole system is heated to \({120^{\circ} {C}}\).
(Given \({\mkern 1mu} {\mkern 1mu} {\alpha _{{\text{brass}}}} = 1.8 \times {10^{ - 50}}{C^{ - 1}},\)
\({\alpha _{{\text{steel}}}} = 1.2 \times {10^{ - 50}}{C^{ - 1}},\)
\({{Y_{{\rm{steel }}}} = 20 + {{10}^{11}}N{m^{ - 2}},{Y_{{\rm{brass }}}}}\) \(\left. { = 1.7 \times {{10}^7}N{m^{ - 2}}} \right)\)
supporting img

1 \(160 \times {10^6}\,N{m^{ - 2}}\)
2 \(130 \times {10^6}\,N{m^{ - 2}}\)
3 \(110 \times {10^6}\,N{m^2}\)
4 \(120 \times {10^6}\,N{m^{ - 2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366801 A steel wire of uniform area \(2\;\,m{m^2}\) is heated upto \(50^\circ C\) and is stretched by tying its ends rigidly. The change in tension when the temperature falls from \(50^\circ C\) to \(30^\circ C\) is (Take \(Y = 2 \times {10^{11}}N{m^{ - 2}},\alpha = 1.1 \times {10^{ - 5^\circ }}{C^{ - 1}}\) )

1 \(5\;N\)
2 \(1.5 \times {10^{10}}\;N\)
3 \(2.5 \times {10^{10}}\;N\)
4 \(88\;N\)
PHXI11:THERMAL PROPERTIES OF MATTER

366798 A rod, of length \(L\) at room temperature and uniform area of cross-section \(A\), is made of a metal having coefficient of linear expansion \(\alpha /^\circ C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \(\Delta TK\). Young's modulus \(Y\), for this metal is

1 \(\frac{{2\;F}}{{\;A\alpha \Delta T}}\)
2 \(\dfrac{F}{A \alpha \Delta T}\)
3 \(\dfrac{F}{2 A \alpha \Delta T}\)
4 \(\frac{F}{{\;A\alpha (\Delta T - 273)}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366799 Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
\(\left(\alpha_{1}, \alpha_{2}=\right.\) linear expansion coefficients \(A_{1}, A_{2}=\) Area of rods \(Y_{1}, Y_{2}=\) Young modulus)
supporting img

1 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{1} Y_{1}}{\alpha_{2} Y_{2}}\)
2 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{1} \alpha_{1} Y_{1}}{L_{2} \alpha_{2} Y_{2}}\)
3 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{2} \alpha_{2} Y_{2}}{L_{1} \alpha_{1} Y_{1}}\)
4 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{2} Y_{2}}{\alpha_{1} Y_{1}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366800 A fine steel wire of length \(4\,m\) is fixed rigidly in a heavy brass frame as shown in figure. It is just taut at \({20^{\circ} {C}}\). Find the tensile stress developed in steel wire if whole system is heated to \({120^{\circ} {C}}\).
(Given \({\mkern 1mu} {\mkern 1mu} {\alpha _{{\text{brass}}}} = 1.8 \times {10^{ - 50}}{C^{ - 1}},\)
\({\alpha _{{\text{steel}}}} = 1.2 \times {10^{ - 50}}{C^{ - 1}},\)
\({{Y_{{\rm{steel }}}} = 20 + {{10}^{11}}N{m^{ - 2}},{Y_{{\rm{brass }}}}}\) \(\left. { = 1.7 \times {{10}^7}N{m^{ - 2}}} \right)\)
supporting img

1 \(160 \times {10^6}\,N{m^{ - 2}}\)
2 \(130 \times {10^6}\,N{m^{ - 2}}\)
3 \(110 \times {10^6}\,N{m^2}\)
4 \(120 \times {10^6}\,N{m^{ - 2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366801 A steel wire of uniform area \(2\;\,m{m^2}\) is heated upto \(50^\circ C\) and is stretched by tying its ends rigidly. The change in tension when the temperature falls from \(50^\circ C\) to \(30^\circ C\) is (Take \(Y = 2 \times {10^{11}}N{m^{ - 2}},\alpha = 1.1 \times {10^{ - 5^\circ }}{C^{ - 1}}\) )

1 \(5\;N\)
2 \(1.5 \times {10^{10}}\;N\)
3 \(2.5 \times {10^{10}}\;N\)
4 \(88\;N\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI11:THERMAL PROPERTIES OF MATTER

366798 A rod, of length \(L\) at room temperature and uniform area of cross-section \(A\), is made of a metal having coefficient of linear expansion \(\alpha /^\circ C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \(\Delta TK\). Young's modulus \(Y\), for this metal is

1 \(\frac{{2\;F}}{{\;A\alpha \Delta T}}\)
2 \(\dfrac{F}{A \alpha \Delta T}\)
3 \(\dfrac{F}{2 A \alpha \Delta T}\)
4 \(\frac{F}{{\;A\alpha (\Delta T - 273)}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366799 Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
\(\left(\alpha_{1}, \alpha_{2}=\right.\) linear expansion coefficients \(A_{1}, A_{2}=\) Area of rods \(Y_{1}, Y_{2}=\) Young modulus)
supporting img

1 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{1} Y_{1}}{\alpha_{2} Y_{2}}\)
2 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{1} \alpha_{1} Y_{1}}{L_{2} \alpha_{2} Y_{2}}\)
3 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{2} \alpha_{2} Y_{2}}{L_{1} \alpha_{1} Y_{1}}\)
4 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{2} Y_{2}}{\alpha_{1} Y_{1}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366800 A fine steel wire of length \(4\,m\) is fixed rigidly in a heavy brass frame as shown in figure. It is just taut at \({20^{\circ} {C}}\). Find the tensile stress developed in steel wire if whole system is heated to \({120^{\circ} {C}}\).
(Given \({\mkern 1mu} {\mkern 1mu} {\alpha _{{\text{brass}}}} = 1.8 \times {10^{ - 50}}{C^{ - 1}},\)
\({\alpha _{{\text{steel}}}} = 1.2 \times {10^{ - 50}}{C^{ - 1}},\)
\({{Y_{{\rm{steel }}}} = 20 + {{10}^{11}}N{m^{ - 2}},{Y_{{\rm{brass }}}}}\) \(\left. { = 1.7 \times {{10}^7}N{m^{ - 2}}} \right)\)
supporting img

1 \(160 \times {10^6}\,N{m^{ - 2}}\)
2 \(130 \times {10^6}\,N{m^{ - 2}}\)
3 \(110 \times {10^6}\,N{m^2}\)
4 \(120 \times {10^6}\,N{m^{ - 2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366801 A steel wire of uniform area \(2\;\,m{m^2}\) is heated upto \(50^\circ C\) and is stretched by tying its ends rigidly. The change in tension when the temperature falls from \(50^\circ C\) to \(30^\circ C\) is (Take \(Y = 2 \times {10^{11}}N{m^{ - 2}},\alpha = 1.1 \times {10^{ - 5^\circ }}{C^{ - 1}}\) )

1 \(5\;N\)
2 \(1.5 \times {10^{10}}\;N\)
3 \(2.5 \times {10^{10}}\;N\)
4 \(88\;N\)
PHXI11:THERMAL PROPERTIES OF MATTER

366798 A rod, of length \(L\) at room temperature and uniform area of cross-section \(A\), is made of a metal having coefficient of linear expansion \(\alpha /^\circ C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \(\Delta TK\). Young's modulus \(Y\), for this metal is

1 \(\frac{{2\;F}}{{\;A\alpha \Delta T}}\)
2 \(\dfrac{F}{A \alpha \Delta T}\)
3 \(\dfrac{F}{2 A \alpha \Delta T}\)
4 \(\frac{F}{{\;A\alpha (\Delta T - 273)}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366799 Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
\(\left(\alpha_{1}, \alpha_{2}=\right.\) linear expansion coefficients \(A_{1}, A_{2}=\) Area of rods \(Y_{1}, Y_{2}=\) Young modulus)
supporting img

1 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{1} Y_{1}}{\alpha_{2} Y_{2}}\)
2 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{1} \alpha_{1} Y_{1}}{L_{2} \alpha_{2} Y_{2}}\)
3 \(\dfrac{A_{1}}{A_{2}}=\dfrac{L_{2} \alpha_{2} Y_{2}}{L_{1} \alpha_{1} Y_{1}}\)
4 \(\dfrac{A_{1}}{A_{2}}=\dfrac{\alpha_{2} Y_{2}}{\alpha_{1} Y_{1}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366800 A fine steel wire of length \(4\,m\) is fixed rigidly in a heavy brass frame as shown in figure. It is just taut at \({20^{\circ} {C}}\). Find the tensile stress developed in steel wire if whole system is heated to \({120^{\circ} {C}}\).
(Given \({\mkern 1mu} {\mkern 1mu} {\alpha _{{\text{brass}}}} = 1.8 \times {10^{ - 50}}{C^{ - 1}},\)
\({\alpha _{{\text{steel}}}} = 1.2 \times {10^{ - 50}}{C^{ - 1}},\)
\({{Y_{{\rm{steel }}}} = 20 + {{10}^{11}}N{m^{ - 2}},{Y_{{\rm{brass }}}}}\) \(\left. { = 1.7 \times {{10}^7}N{m^{ - 2}}} \right)\)
supporting img

1 \(160 \times {10^6}\,N{m^{ - 2}}\)
2 \(130 \times {10^6}\,N{m^{ - 2}}\)
3 \(110 \times {10^6}\,N{m^2}\)
4 \(120 \times {10^6}\,N{m^{ - 2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366801 A steel wire of uniform area \(2\;\,m{m^2}\) is heated upto \(50^\circ C\) and is stretched by tying its ends rigidly. The change in tension when the temperature falls from \(50^\circ C\) to \(30^\circ C\) is (Take \(Y = 2 \times {10^{11}}N{m^{ - 2}},\alpha = 1.1 \times {10^{ - 5^\circ }}{C^{ - 1}}\) )

1 \(5\;N\)
2 \(1.5 \times {10^{10}}\;N\)
3 \(2.5 \times {10^{10}}\;N\)
4 \(88\;N\)