Q. No.A metal string \(A\) \(M.\) \(B\) \(A\) \(B\) \(A\) \(Y_A/Y_B\)
1. \(1\)
2. \(4\)
3. \(8\)
4. \(6\)
1. \(1\)
2. \(4\)
3. \(8\)
4. \(6\)
Subtopic: Young's modulus |
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Figure represents the extension \((\Delta{l})\) of a wire of length \(1\) meter, suspended from the ceiling of the room at one end with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}~ \text{m}^{2}\) then the Young's modulus of the wire is: (in \(\text{N/m}^2\))
1. \(1.0 \times 10^{11}\)
2. \(2.0 \times 10^{10} \)
3. \(1.0 \times 10^{10} \)
4. \(2.0 \times 10^{11}\)
1. \(1.0 \times 10^{11}\)
2. \(2.0 \times 10^{10} \)
3. \(1.0 \times 10^{10} \)
4. \(2.0 \times 10^{11}\)
Subtopic: Young's modulus |
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The two wires \(A\) and \(B\) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \(A\) and wire \(B\) is \(20/11\). When the joined wire is kept under certain tension the elongation in the wires \(A\) and \(B\) are equal. If the length of wire \(A\) is \(2.2~\text{m},\) then the length of wire \(B\) is: (in m)
1. \(1.1\)
2. \(2.22\)
3. \(1.21\)
4. \(4.44\)
1. \(1.1\)
2. \(2.22\)
3. \(1.21\)
4. \(4.44\)
Subtopic: Young's modulus |
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The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100~\text{N}\) is applied to the wire, the extension in length is \(0.5\) cm, measured by a micrometer of least count \(0.001\) cm. The error in the measured Young's modulus is \(\alpha \times 10^{9} ~\text{N/m}^2 \)
(Ignore the contribution of the load to Young's modulus error calculation)
1. \(1.3\)
2. \(1.65\)
3. \(0.13\)
4. \(0.25\)
(Ignore the contribution of the load to Young's modulus error calculation)
1. \(1.3\)
2. \(1.65\)
3. \(0.13\)
4. \(0.25\)
Subtopic: Young's modulus |
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The Young's modulus of steel wire of radius \(r\) and length \( L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\).
1. increases by two times
2. reduces by half
3. remains unchanged
4. becomes one fourth
1. increases by two times
2. reduces by half
3. remains unchanged
4. becomes one fourth
Subtopic: Young's modulus |
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A string \(A\) \(2\times 10^{10}~\text{N/m}^2\)
(radius of both the strings is \(0.2~\text{mm}\) and acceleration due to gravity \(=10~\text{m/s}^2\)) (Mass of both strings is to be neglected as compared to the mass of load)
1. \(3\)
2. \(2\)
3. \(1.9\)
4. \(1\)
(radius of both the strings is \(0.2~\text{mm}\) and acceleration due to gravity \(=10~\text{m/s}^2\)) (Mass of both strings is to be neglected as compared to the mass of load)
1. \(3\)
2. \(2\)
3. \(1.9\)
4. \(1\)
Subtopic: Young's modulus |
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Two wires, \(A\) and \(B ,\) made of different materials, have lengths of \(6.0~\text{cm}\) and \(5.4~\text{cm},\) and cross-sectional areas of \(3.0 \times10^{-5} ~\text{m}^2 \) and \(4.5 \times10^{-5} ~\text{m}^2 ,\) respectively. If both wires are subjected to the same tensile force and undergo equal extensions, and the ratio of their Young’s moduli is \(Y_1:Y_B=x:3,\) what is the value of \(x\)?
1. \(1\)
2. \(4\)
3. \(2\)
4. \(5\)
1. \(1\)
2. \(4\)
3. \(2\)
4. \(5\)
Subtopic: Young's modulus |
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A \(3~\text{m}\) long wire of radius \(3~\text{mm} \) shows an extension of \(0.1~\text{mm} \) when loaded vertically by a mass of \(50~\text{kg} \) in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is \(P × 10^{11}~\text{Nm}^{-2} , \) where the value of \(P \) is:
(Take \(g=3π~ \text{m/s}^2\))
1. \(5\)
2. \(10 \)
3. \(25\)
4. \(2.5\)
(Take \(g=3π~ \text{m/s}^2\))
1. \(5\)
2. \(10 \)
3. \(25\)
4. \(2.5\)
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Two wires \(A\) and \(B \) are made of same material having ratio of lengths \(\dfrac {L_A}{L_B} = \dfrac{1}{3} \) and their diameters ratio \(\dfrac{d_A}{d_B} = 2.\) If both the wires are stretched using same force, what would be the ratio of their respective elongations.
1. \(1:12\)
2. \(3:4\)
3. \(1:6\)
4. \(1:3\)
1. \(1:12\)
2. \(3:4\)
3. \(1:6\)
4. \(1:3\)
Subtopic: Young's modulus |
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A steel wire of length \(2 \text{ m}\) and Young's modulus \(2.0 \times 10^{11} ~\text{Nm}^{-2}\) is stretched by a force. If Poisson ratio and transverse strain for the wire are \(0.2\) and \(10^{-3}\) respectively, then the elastic potential energy density of the wire is: (in \(\times10^5 \))(in \(SI\) units).
1. \(25 \times 10^2 \)
2. \(25 \times 10^3 \)
3. \(25 \times 10^5 \)
4. \(25 \times 10^4 \)
1. \(25 \times 10^2 \)
2. \(25 \times 10^3 \)
3. \(25 \times 10^5 \)
4. \(25 \times 10^4 \)
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