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1.

The ratio of lengths of two rods \(A\) and \(B\) of the same material is \(1:2\) and the ratio of their radii is \(2:1\). The ratio of modulus of rigidity of \(A\) and \(B\) will be:

1.	\(4:1\)	2.	\(16:1\)
3.	\(8:1\)	4.	\(1:1\)

2.

Two wires of copper having length in the ratio of \(4:1\) and radii ratio of \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two will be:

1.	\(1:16\)	2.	\(16:1\)
3.	\(1:64\)	4.	\(64:1\)

3.

The figure shows the stress-strain curve for a given material. The approximate yield strength for this material is:
         
1. \(3\times10^8~\text{N/m}^2\)
2. \(2\times10^8~\text{N/m}^2\)
3. \(4\times10^8~\text{N/m}^2\)
4. \(1\times10^8~\text{N/m}^2\)

4.

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

5.

A square lead slab of side \(50~\text{cm}\) and thickness \(10~\text{cm}\) 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.	\(0.16~\text{mm}\)	2.	\(1.8~\text{mm}\)
3.	\(18~\text{mm}\)	4.	\(16~\text{mm}\)

6. The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length \(100~\text{cm}\) to stretch it by \(1~\text{mm}\) is:
(given: Young's modulus of the wire = \(Y=2.0\times 10^{11}~\text{N/m}^2\))
1. \(10^{11}~\text{J/m}^3\)
2. \(10^{17}~\text{J/m}^3\)
3. \(10^{7}~\text{J/m}^3\)
4. \(10^{5}~\text{J/m}^3\)

7.

When strain is produced in a body within elastic limit, its internal energy:
1. Remains constant                  
2. Decreases
3. Increases                               
4. None of the above

8. A rod of length \(1.05\) m having negligible mass is supported at its ends by two wires of steel (wire \(A\)) and aluminium (wire \(B\)) of equal lengths as shown in the figure. The cross-sectional areas of wires \(A\) and \(B\) are \(1.0~\text{mm}^2\) and \(2.0~\text{mm}^2\) respectively. At what point along the rod should a mass m be suspended in order to produce equal stresses in both steel and aluminium wires?
           

1.	\(0.7\) m from wire \(A\)
2.	\(0.07\) m from wire \(A\)
3.	\(7.0\) m from wire \(A\)
4.	\(0.007\) m from wire \(A\)

9.

A uniform cylinder rod of length \(L\), cross-sectional area \(A\) and Young's modulus \(Y\) is acted upon by the forces, as shown in the figure. The elongation of the rod is:
           
1. \(\frac{3FL}{5AY}\)
2. \(\frac{2FL}{5AY}\)
3. \(\frac{2FL}{8AY}\)
4. \(\frac{8FL}{3AY}\)

10. Choose the correct statement.

1.	Breaking stress does not depend on the area of cross-section.
2.	\(B_{\text {solid }}>{B}_{\text {gas }}>{B}_{\text {liquid }}\) where \(B\) is the bulk modulus.
3.	Breaking load does not depend on the area of cross-section.
4.	Young's modulus always decreases on decreasing the temperature.