Q. No.A boy’s catapult is made of rubber cord which is \(42~\text{cm}\) long, with \(6~\text{mm}\) diameter of a cross-section and of negligible mass. The boy keeps a stone weighing \(0.02~\text{kg}\) on it and stretches the cord by \(20~\text{cm}\) by applying a constant force. When released, the stone flies off with a velocity of \(20~\text{ms}^{-1}.\) Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:
1. \( 10^3 ~\text{Nm}^{-2} \)
2. \(10^4~\text{Nm}^{-2} \)
3. \( 10^6 ~\text{Nm}^{-2} \)
4. \( 10^8~\text{Nm}^{-2} \)
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. \(\frac {1} {\sqrt{2}}~\text{mm}\)
3. \(2\sqrt{2} ~\text{mm}\)
4. \(2~\text{mm}\)
(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
1. \(\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}} \)
2. \(\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2} \)
3. \(2 \mathrm{~L}_{1}-\mathrm{L}_{2} \)
4. \(3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}\)
1. \(3~\text{cm}\)
2. \(5~\text{cm}\)
3. \(10~\text{cm}\)
4. \(6~\text{cm}\)
(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
1. \(360\)
2. \(180\)
3. \(1080\)
4. \(154\)
(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
| 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. |
1. \(8:1\)
2. \(1:12\)
3. \(1:8\)
4. \(9:2\)
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