# A copper wire of length $$2.2$$ m and a steel wire of length $$1.6$$ m, both of diameter $$3.0$$ mm, are connected end to end. When stretched by a load, the net elongation is found to be $$0.70$$ mm. The load applied is: $$Y_C = 1.1\times 10^{11}~\text{Nm}^{-2}~\text{and}~Y_S = 2.0\times 10^{11}~\text{Nm}^{-2}$$ 1. $$1.8\times 10^{2}~\text{N}$$ 2. $$1.8~\text{N}$$ 3. $$1.8\times 10^{3}~\text{N}$$ 4. $$18\times 10^{3}~\text{N}$$

Subtopic:  Hooke's Law |
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In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back (as shown in the figure below). The combined mass of all the persons performing the act, and the tables, plaques, etc. involved is $$280~\text{kg}$$. The mass of the performer lying on his back at the bottom of the pyramid is $$60~\text{kg}$$. Each thighbone (femur) of this performer has a length of $$50~\text{cm}$$ and an effective radius of $$2.0~\text{cm}$$. The amount by which each thighbone gets compressed under the extra load is: (The Young’s modulus for bone is given by, $$Y = 9.4\times 10^9~\text{N/m}^{2}$$)

 1 $$4.55\times 10^{-5}~\text{cm}$$ 2 $$5.45\times 10^{-3}~\text{cm}$$ 3 $$5.45\times 10^{-5}~\text{cm}$$ 4 $$4.55\times 10^{-3}~\text{cm}$$
Subtopic:  Stress - Strain |
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A square lead slab of side $$50$$ cm and thickness $$10$$ cm is subject to a shearing force (on its narrow face) of $$9.0\times 10^{4}~\text{N}$$$\mathrm{}$. The lower edge is riveted to the floor as shown in the figure below. How much will the upper edge be displaced? (Shear modulus of lead $$= 5.6\times 10^{9}~\text{Nm}^{-2}$$)

 1 $$0.16$$ mm 2 $$1.8$$ mm 3 $$18$$ mm 4 $$16$$ mm
Subtopic:  Shear and bulk modulus |
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The average depth of the Indian Ocean is about $$3000$$ m. The fractional compression, $$\dfrac{\Delta V}{V},$$ of water at the bottom of the ocean is? (Given that the bulk modulus of water is $$2.2\times10^{9}$$ Nm–2 and $$g=10$$ ms–2)
1. $$1.36\times10^{-3}$$
2. $$2.36\times10^{-3}$$
3. $$1.36\times10^{-2}$$
4. $$2.36\times10^{-2}$$

Subtopic:  Shear and bulk modulus |
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A structural steel rod has a radius of $$10~\text{mm}$$ and a length of $$1.0~\text{m}.$$ A $$100~\text{kN}$$ force stretches it along its length. The stress produced and the elongation in the rod, respectively, are?
(Young’s modulus of structural steel is
$$2.0\times 10^{11}~\text{Nm}^{-2}.)$$
1. $$3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{mm}$$
2. $$3.18\times 10^{8}~\text{Nm}^{-2}~\text{and}~1.59~\text{m}$$
3. $$3.18\times 10^{8}~\text{Nm}^{-2}~\text{and}~1.59~\text{mm}$$
4. $$3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{m}$$

Subtopic:  Hooke's Law |
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