Elastic Moduli
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369793 A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If \(L, \alpha\) and \(Y\) respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by \(\Delta T\), the longitudinal stress developed in the rod is

1 inversely proportional to \(\alpha\)
2 inversely proportional to \(Y\)
3 directly proportional to \(\dfrac{\Delta T}{Y}\)
4 independent of \(L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369794 A steel ring of radius \(r\) and cross-section area ' \(A\) ' is fitted onto a wooden disc of radius \(R(R > r)\). IF Young's modulus be E, then the force with which the steel ring is expanded is

1 \(A E\left(\dfrac{R-r}{r}\right)\)
2 \(A E \dfrac{R}{r}\)
3 \(\dfrac{E r}{A R}\)
4 \(\dfrac{E}{A}\left(\dfrac{R-r}{A}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369795 A wire of length \(L\) and radius \(r\) is rigidly fixed at one end. On stretching the other end of the wire with a force \(F\), the increase in length is \(l\). If another wire of the same material but double the length and radius is stretched with a force \(2\;F\), then increase in length is

1 \(\dfrac{l}{4}\)
2 \(2 l\)
3 \(\dfrac{l}{2}\)
4 \(l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369796 Under the same load, wire \(A\) having length \(5.0\;m\) and the cross section \(2.5 \times {10^{ - 5}}\;{m^2}\) stretches uniformly by same amount as another wire \(B\) of length \(6.0\;m\) and a cross-section of \(3.0 \times {10^{ - 5}}\;{m^2}\) stretches. The ratio of the Young's modulus of wire \(A\) to that of wire \(B\) will be

1 \(1: 10\)
2 \(1: 1\)
3 \(1: 4\)
4 \(1: 2\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369793 A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If \(L, \alpha\) and \(Y\) respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by \(\Delta T\), the longitudinal stress developed in the rod is

1 inversely proportional to \(\alpha\)
2 inversely proportional to \(Y\)
3 directly proportional to \(\dfrac{\Delta T}{Y}\)
4 independent of \(L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369794 A steel ring of radius \(r\) and cross-section area ' \(A\) ' is fitted onto a wooden disc of radius \(R(R > r)\). IF Young's modulus be E, then the force with which the steel ring is expanded is

1 \(A E\left(\dfrac{R-r}{r}\right)\)
2 \(A E \dfrac{R}{r}\)
3 \(\dfrac{E r}{A R}\)
4 \(\dfrac{E}{A}\left(\dfrac{R-r}{A}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369795 A wire of length \(L\) and radius \(r\) is rigidly fixed at one end. On stretching the other end of the wire with a force \(F\), the increase in length is \(l\). If another wire of the same material but double the length and radius is stretched with a force \(2\;F\), then increase in length is

1 \(\dfrac{l}{4}\)
2 \(2 l\)
3 \(\dfrac{l}{2}\)
4 \(l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369796 Under the same load, wire \(A\) having length \(5.0\;m\) and the cross section \(2.5 \times {10^{ - 5}}\;{m^2}\) stretches uniformly by same amount as another wire \(B\) of length \(6.0\;m\) and a cross-section of \(3.0 \times {10^{ - 5}}\;{m^2}\) stretches. The ratio of the Young's modulus of wire \(A\) to that of wire \(B\) will be

1 \(1: 10\)
2 \(1: 1\)
3 \(1: 4\)
4 \(1: 2\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369793 A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If \(L, \alpha\) and \(Y\) respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by \(\Delta T\), the longitudinal stress developed in the rod is

1 inversely proportional to \(\alpha\)
2 inversely proportional to \(Y\)
3 directly proportional to \(\dfrac{\Delta T}{Y}\)
4 independent of \(L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369794 A steel ring of radius \(r\) and cross-section area ' \(A\) ' is fitted onto a wooden disc of radius \(R(R > r)\). IF Young's modulus be E, then the force with which the steel ring is expanded is

1 \(A E\left(\dfrac{R-r}{r}\right)\)
2 \(A E \dfrac{R}{r}\)
3 \(\dfrac{E r}{A R}\)
4 \(\dfrac{E}{A}\left(\dfrac{R-r}{A}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369795 A wire of length \(L\) and radius \(r\) is rigidly fixed at one end. On stretching the other end of the wire with a force \(F\), the increase in length is \(l\). If another wire of the same material but double the length and radius is stretched with a force \(2\;F\), then increase in length is

1 \(\dfrac{l}{4}\)
2 \(2 l\)
3 \(\dfrac{l}{2}\)
4 \(l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369796 Under the same load, wire \(A\) having length \(5.0\;m\) and the cross section \(2.5 \times {10^{ - 5}}\;{m^2}\) stretches uniformly by same amount as another wire \(B\) of length \(6.0\;m\) and a cross-section of \(3.0 \times {10^{ - 5}}\;{m^2}\) stretches. The ratio of the Young's modulus of wire \(A\) to that of wire \(B\) will be

1 \(1: 10\)
2 \(1: 1\)
3 \(1: 4\)
4 \(1: 2\)
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PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369793 A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If \(L, \alpha\) and \(Y\) respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by \(\Delta T\), the longitudinal stress developed in the rod is

1 inversely proportional to \(\alpha\)
2 inversely proportional to \(Y\)
3 directly proportional to \(\dfrac{\Delta T}{Y}\)
4 independent of \(L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369794 A steel ring of radius \(r\) and cross-section area ' \(A\) ' is fitted onto a wooden disc of radius \(R(R > r)\). IF Young's modulus be E, then the force with which the steel ring is expanded is

1 \(A E\left(\dfrac{R-r}{r}\right)\)
2 \(A E \dfrac{R}{r}\)
3 \(\dfrac{E r}{A R}\)
4 \(\dfrac{E}{A}\left(\dfrac{R-r}{A}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369795 A wire of length \(L\) and radius \(r\) is rigidly fixed at one end. On stretching the other end of the wire with a force \(F\), the increase in length is \(l\). If another wire of the same material but double the length and radius is stretched with a force \(2\;F\), then increase in length is

1 \(\dfrac{l}{4}\)
2 \(2 l\)
3 \(\dfrac{l}{2}\)
4 \(l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369796 Under the same load, wire \(A\) having length \(5.0\;m\) and the cross section \(2.5 \times {10^{ - 5}}\;{m^2}\) stretches uniformly by same amount as another wire \(B\) of length \(6.0\;m\) and a cross-section of \(3.0 \times {10^{ - 5}}\;{m^2}\) stretches. The ratio of the Young's modulus of wire \(A\) to that of wire \(B\) will be

1 \(1: 10\)
2 \(1: 1\)
3 \(1: 4\)
4 \(1: 2\)