Elastic Moduli
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369810 A student performs an experiment to determine the Young's modulus of a wire, exactly \(2 m\) long, by searle's method. The student measures the extension in the length of the wire to be \(0.8\;mm\) with an uncertainty of \( \pm 0.05\;mm\) at a load of exactly \(1.0\;kg\). The student also,measures the diameter of the wire to be \(0.4\;mm\) with an uncertainty \( \pm 0.01\;mm.\,{\text{Take}}\,g = 9.8\;m/{s^2}\) (exact). The Young's modulus obtained from the reading is

1 \((2.0 \pm 0.3) \times {10^{11}}\;N/{m^2}\)
2 \((2.0 \pm 0.2) \times {10^{11}}\;N/{m^2}\)
3 \((2.0 \pm 0.05) \times {10^{11}}\;N/{m^2}\)
4 \((2.0 \pm 0.1) \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369811 How much force is required to produce an increase of \({0.2 \%}\) in the length of a brass wire of diameter \(0.6\,mm\) ? Given Young's modulus for brass \({=0.9 \times 10^{11} {~N} / {m}^{2}}\)

1 nearly 17 \(N\)
2 nearly 51 \(N\)
3 nearly 34 \(N\)
4 nearly 68 \(N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369812 A uniform rod of mass \(m\), length \(L\), area of crosssection A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity \(\omega\) in a horizontal plane. If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is

1 \(\dfrac{1}{4} \dfrac{m \omega^{2} L^{3}}{Y A}\)
2 \(\dfrac{1}{3} \dfrac{m \omega^{2} L^{3}}{Y A}\)
3 \(\dfrac{1}{9} \dfrac{m \omega^{2} L^{3}}{Y A}\)
4 \(\dfrac{1}{18} \dfrac{m \omega^{2} L}{Y A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369813 The ratio of diameters of two wires of same material is \(n: 1\). The length of each wire is \(4\,m\). On applying the same load, the ratio of increase in length of the wire will be \((n>1)\)

1 \(1 / n^{2}\) times
2 \(n\) times
3 \(2 n\) times
4 \((2 n+1)\) times
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369810 A student performs an experiment to determine the Young's modulus of a wire, exactly \(2 m\) long, by searle's method. The student measures the extension in the length of the wire to be \(0.8\;mm\) with an uncertainty of \( \pm 0.05\;mm\) at a load of exactly \(1.0\;kg\). The student also,measures the diameter of the wire to be \(0.4\;mm\) with an uncertainty \( \pm 0.01\;mm.\,{\text{Take}}\,g = 9.8\;m/{s^2}\) (exact). The Young's modulus obtained from the reading is

1 \((2.0 \pm 0.3) \times {10^{11}}\;N/{m^2}\)
2 \((2.0 \pm 0.2) \times {10^{11}}\;N/{m^2}\)
3 \((2.0 \pm 0.05) \times {10^{11}}\;N/{m^2}\)
4 \((2.0 \pm 0.1) \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369811 How much force is required to produce an increase of \({0.2 \%}\) in the length of a brass wire of diameter \(0.6\,mm\) ? Given Young's modulus for brass \({=0.9 \times 10^{11} {~N} / {m}^{2}}\)

1 nearly 17 \(N\)
2 nearly 51 \(N\)
3 nearly 34 \(N\)
4 nearly 68 \(N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369812 A uniform rod of mass \(m\), length \(L\), area of crosssection A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity \(\omega\) in a horizontal plane. If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is

1 \(\dfrac{1}{4} \dfrac{m \omega^{2} L^{3}}{Y A}\)
2 \(\dfrac{1}{3} \dfrac{m \omega^{2} L^{3}}{Y A}\)
3 \(\dfrac{1}{9} \dfrac{m \omega^{2} L^{3}}{Y A}\)
4 \(\dfrac{1}{18} \dfrac{m \omega^{2} L}{Y A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369813 The ratio of diameters of two wires of same material is \(n: 1\). The length of each wire is \(4\,m\). On applying the same load, the ratio of increase in length of the wire will be \((n>1)\)

1 \(1 / n^{2}\) times
2 \(n\) times
3 \(2 n\) times
4 \((2 n+1)\) times
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369810 A student performs an experiment to determine the Young's modulus of a wire, exactly \(2 m\) long, by searle's method. The student measures the extension in the length of the wire to be \(0.8\;mm\) with an uncertainty of \( \pm 0.05\;mm\) at a load of exactly \(1.0\;kg\). The student also,measures the diameter of the wire to be \(0.4\;mm\) with an uncertainty \( \pm 0.01\;mm.\,{\text{Take}}\,g = 9.8\;m/{s^2}\) (exact). The Young's modulus obtained from the reading is

1 \((2.0 \pm 0.3) \times {10^{11}}\;N/{m^2}\)
2 \((2.0 \pm 0.2) \times {10^{11}}\;N/{m^2}\)
3 \((2.0 \pm 0.05) \times {10^{11}}\;N/{m^2}\)
4 \((2.0 \pm 0.1) \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369811 How much force is required to produce an increase of \({0.2 \%}\) in the length of a brass wire of diameter \(0.6\,mm\) ? Given Young's modulus for brass \({=0.9 \times 10^{11} {~N} / {m}^{2}}\)

1 nearly 17 \(N\)
2 nearly 51 \(N\)
3 nearly 34 \(N\)
4 nearly 68 \(N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369812 A uniform rod of mass \(m\), length \(L\), area of crosssection A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity \(\omega\) in a horizontal plane. If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is

1 \(\dfrac{1}{4} \dfrac{m \omega^{2} L^{3}}{Y A}\)
2 \(\dfrac{1}{3} \dfrac{m \omega^{2} L^{3}}{Y A}\)
3 \(\dfrac{1}{9} \dfrac{m \omega^{2} L^{3}}{Y A}\)
4 \(\dfrac{1}{18} \dfrac{m \omega^{2} L}{Y A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369813 The ratio of diameters of two wires of same material is \(n: 1\). The length of each wire is \(4\,m\). On applying the same load, the ratio of increase in length of the wire will be \((n>1)\)

1 \(1 / n^{2}\) times
2 \(n\) times
3 \(2 n\) times
4 \((2 n+1)\) times
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369810 A student performs an experiment to determine the Young's modulus of a wire, exactly \(2 m\) long, by searle's method. The student measures the extension in the length of the wire to be \(0.8\;mm\) with an uncertainty of \( \pm 0.05\;mm\) at a load of exactly \(1.0\;kg\). The student also,measures the diameter of the wire to be \(0.4\;mm\) with an uncertainty \( \pm 0.01\;mm.\,{\text{Take}}\,g = 9.8\;m/{s^2}\) (exact). The Young's modulus obtained from the reading is

1 \((2.0 \pm 0.3) \times {10^{11}}\;N/{m^2}\)
2 \((2.0 \pm 0.2) \times {10^{11}}\;N/{m^2}\)
3 \((2.0 \pm 0.05) \times {10^{11}}\;N/{m^2}\)
4 \((2.0 \pm 0.1) \times {10^{11}}\;N/{m^2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369811 How much force is required to produce an increase of \({0.2 \%}\) in the length of a brass wire of diameter \(0.6\,mm\) ? Given Young's modulus for brass \({=0.9 \times 10^{11} {~N} / {m}^{2}}\)

1 nearly 17 \(N\)
2 nearly 51 \(N\)
3 nearly 34 \(N\)
4 nearly 68 \(N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369812 A uniform rod of mass \(m\), length \(L\), area of crosssection A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity \(\omega\) in a horizontal plane. If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is

1 \(\dfrac{1}{4} \dfrac{m \omega^{2} L^{3}}{Y A}\)
2 \(\dfrac{1}{3} \dfrac{m \omega^{2} L^{3}}{Y A}\)
3 \(\dfrac{1}{9} \dfrac{m \omega^{2} L^{3}}{Y A}\)
4 \(\dfrac{1}{18} \dfrac{m \omega^{2} L}{Y A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369813 The ratio of diameters of two wires of same material is \(n: 1\). The length of each wire is \(4\,m\). On applying the same load, the ratio of increase in length of the wire will be \((n>1)\)

1 \(1 / n^{2}\) times
2 \(n\) times
3 \(2 n\) times
4 \((2 n+1)\) times