A wire of cross-section $$A_{1}$$ and length $$l_1$$ breaks when it is under tension $$T_{1};$$ a second wire made of the same material but of cross-section $$A_{2}$$ and length $$l_2$$ breaks under tension $$T_{2}.$$ A third wire of the same material having cross-section $$A,$$ length $$l$$ breaks under tension $$\frac{T_1+T_2}{2}$$. Then,

 1 $$A=\frac{A_1+A_2}{2},~l=\frac{l_1+l_2}{2}$$ 2 $$l=\frac{l_1+l_2}{2}$$ 3 $$A=\frac{A_1+A_2}{2}$$ 4 $$A=\frac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\frac{l_1T_1+l_2T_2}{2(T_1+T_2)}$$
Subtopic:  Young's modulus |
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If two identically shaped rods are joined end to end and compressive forces are applied to the system, the compressive strain will be:

 1 larger in the rod with a larger Young's modulus 2 larger in the rod with a smaller Young's modulus 3 equal in both the rods 4 negative in the rod with a smaller Young's modulus
Subtopic:  Young's modulus |
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A steel wire of length $$4.7$$ m and cross-sectional area $$3.0 \times 10^{-5}$$ m2 is stretched by the same amount as a copper wire of length $$3.5$$ m and cross-sectional area of $$4.0 \times 10^{-5}$$ m2 under a given load. The ratio of Young’s modulus of steel to that of copper is:
1. $$1.79:1$$
2. $$1:1.79$$
3. $$1:1$$
4. $$1.97:1$$

Subtopic:  Young's modulus |
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Two wires of diameter $$0.25$$ cm, one made of steel and the other made of brass are loaded, as shown in the figure. The unloaded length of the steel wire is $$1.5$$ m and that of the brass wire is $$1.0$$ m. The elongation of the steel wire will be:
(Given that Young's modulus of the steel, $$Y_S=2 \times 10^{11}$$ Pa$\mathrm{}$ and Young's modulus of brass, $$Y_B=1 \times 10^{11}$$ Pa)

 1 $$1.5 \times 10^{-4}$$ m 2 $$0.5 \times 10^{-4}$$ m 3 $$3.5 \times 10^{-4}$$ m 4 $$2.5 \times 10^{-4}$$ m
Subtopic:  Young's modulus |
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A rope $$1$$ cm in diameter breaks if the tension in it exceeds $$500$$ N. The maximum tension that may be given to a similar rope of diameter $$2$$ cm is:
1. $$500$$ N
2. $$250$$ N
3. $$1000$$ N
4. $$2000$$ N

Subtopic:  Young's modulus |
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The length of a metal wire is $$l_1$$ when the tension in it is $$T_1$$ and is $$l_2$$ when the tension is $$T_2.$$ The natural length of the wire is:
1. $$\frac{l_{1}+l_{2}}{2}$$

2. $$\sqrt{l_{1} l_{2}}$$

3. $$\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}$$

4. $$\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}$$

Subtopic:  Young's modulus |
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