Q. No.A boy’s catapult is made of a rubber cord \(42~\text{cm}\) long and \(6~\text{mm}\) in diameter. Placing a\(0.02~\text{kg}\) stone on it, the boy stretches the cord by \(20~\text{cm}\) using a constant force. When released, the stone moves off with a velocity of \(20\) m/s. Neglecting the change in cross-sectional area while stretching, the Young’s modulus of the rubber is approximately equal to:
1. \( 10^3 ~\text{N-m}^{-2} \)
2. \(10^4~\text{N-m}^{-2} \)
3. \( 10^6 ~\text{N-m}^{-2} \)
4. \( 10^8~\text{N-m}^{-2} \)
Subtopic: Young's modulus |
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Young's moduli of two wires \(A\) and \(B\) are in the ratio \(10:4\). Wire \(A\) is \(2~\text{m}\) long and has radius \(R\). Wire \(B\) is \(1.6~\text{m}\) long and has radius \(2~\text{mm}\). If the two wires stretch by the same length for a given load, then the value of \(R\) is close to:
| 1. | \(\sqrt{2} ~\text{mm} \) | 2. | \(\dfrac {1} {\sqrt{2}}~\text{mm} \) |
| 3. | \(2\sqrt{2} ~\text{mm} \) | 4. | \(2~\text{mm} \) |
Subtopic: Young's modulus |
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The elongation of a wire on the surface of the Earth is \(10^{-4}\) m. The same wire, of the same dimensions, elongates by \( 6 \times 10^{-5} \) m on another planet. The acceleration due to gravity on the planet will be:
(take acceleration due to gravity on the surface of the Earth as \(10\) m s-2)
1. \(5\) ms-2
2. \(6\) ms-2
3. \(7\) ms-2
4. \(8\) ms-2
(take acceleration due to gravity on the surface of the Earth as \(10\) m s-2)
1. \(5\) ms-2
2. \(6\) ms-2
3. \(7\) ms-2
4. \(8\) ms-2
Subtopic: Young's modulus |
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A wire of natural length \(L\) is suspended vertically from a fixed point. The length changes to \(L_1\) and \(L_2\) when masses \(1\) kg and \(2\) kg are suspended, respectively, from its free end. The value of \(L\) is:
| 1. | \(\sqrt{L_1L_2} \) | 2. | \(\dfrac{L_1+L_2}{2}\) |
| 3. | \(2L_1-L_2 \) | 4. | \(3L_1-2L_2\) |
Subtopic: Young's modulus |
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A wire of length \(L\) and radius \(r \) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(F,\) its length increases by \(5~\text{cm}. \) Another wire of the same material of length \(4L\) and radius \(4r \) is pulled by a force \(4F \) under the same conditions. The increase in length of this wire is:
1. \(3~\text{cm}\)
2. \(5~\text{cm}\)
3. \(10~\text{cm}\)
4. \(6~\text{cm}\)
1. \(3~\text{cm}\)
2. \(5~\text{cm}\)
3. \(10~\text{cm}\)
4. \(6~\text{cm}\)
Subtopic: Young's modulus |
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A uniform heavy rod of mass \(20\) kg, cross-sectional area of \(0.4\) m2 and length of \(20\) m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is:
(Given: Young’s modulus \(Y=2\times 10^{11}\) N-m–2 and \(g=10~\text{ms}^{–2 }\) )
1. \(12\times 10^{-9}\) m
2. \(30\times 10^{-9}\) m
3. \(25\times 10^{-9}\) m
4. \(35\times 10^{-9}\) m
(Given: Young’s modulus \(Y=2\times 10^{11}\) N-m–2 and \(g=10~\text{ms}^{–2 }\) )
1. \(12\times 10^{-9}\) m
2. \(30\times 10^{-9}\) m
3. \(25\times 10^{-9}\) m
4. \(35\times 10^{-9}\) m
Subtopic: Young's modulus |
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A steel wire of length \(3.2\) m (\(Y_S=2.0 \times 10^{11}\) N m–2 ) and a copper wire of length \(4.4\) m (\(Y_C=1.1 \times 10^{11}\) N m–2 ), both having a radius \(1.4\) mm, are connected end to end. When a load is applied, the net stretch of the combined wires is found to be \(1.4\) mm. The magnitude of the load applied, in Newtons, will be: \(\left (\text{use},~\pi=\dfrac{22}{7} \right ) \)
1. \(360\)
2. \(180\)
3. \(1080\)
4. \(154\)
1. \(360\)
2. \(180\)
3. \(1080\)
4. \(154\)
Subtopic: Young's modulus |
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The force required to stretch a wire of cross-section \(1\) cm2 to double its length will be:
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
Subtopic: Young's modulus |
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If the length of a wire is doubled and its radius is halved compared to their respective initial values, then, Young’s modulus of the material of the wire will:
| 1. | remain the same. |
| 2. | become \(8\) times its initial value. |
| 3. | become \({1 \over 4}\)th of its initial value. |
| 4. | become \(4\) times its initial value. |
Subtopic: Young's modulus |
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Wire \({A}\) and \({B}\) have their Young's modulii in the ratio \(1:3\) area of the cross-section in the ratio of \(1:2\) and lengths in the ratio of \(3:4.\) If the same force is applied on the two wires to elongate then the ratio of elongation is equal to:
1. \(8:1\)
2. \(1:12\)
3. \(1:8\)
4. \(9:2\)
1. \(8:1\)
2. \(1:12\)
3. \(1:8\)
4. \(9:2\)
Subtopic: Young's modulus |
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