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1.

The average depth of the Indian Ocean is about \(3000~\text m.\) The fractional compression \(\frac{\Delta V}{V},\) of water at the bottom of the ocean is? 
(Given that the bulk modulus of water is \(2.2\times10^{9}~\text{Nm}^{-2}\) and \(g=10~\text{ms}^{-2}\))
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)

2.

A steel wire of length \(4.7~\text m\) and cross-sectional area \(3.0 \times 10^{-5}~\text{m}^2\) is stretched by the same amount as a copper wire of length \(3.5~\text m\) and cross-sectional area of \(4.0 \times 10^{-5}~\text m^2\) 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. \(1.97:1\)

3.

The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. Young’s modulus of material \(A\) is:
(the graphs are drawn to the same scale)
                       

1.	equal to material \(B\)
2.	less than material \(B\)
3.	greater than material \(B\)
4.	can't say

4.

The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. The strength of the material \(A\) is:
(The graphs are drawn to the same scale)
       

1.	greater than material \(B\)
2.	equal to material \(B\)
3.	less than material \(B\)
4.	insufficient data

5.

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

6. 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 \(A\)

7.

What is the density of water at a depth where pressure is \(80.0\) atm, given that its density at the surface is \(1.03\times10^{3}~\text{kg m}^{-3}\)?

1.	\(0 . 021 \times 10^{3}~\text{kg m}^{-3}\)	2.	\(4.022 \times10^{3}~\text{kg m}^{-3}\)
3.	\(3.034 \times 10^{3}~\text{kg m}^{-3}\)	4.	\(1.034 \times 10^{3}~\text{kg m}^{-3}\)

8.

A mild steel wire of length \(2L\) and cross-sectional area \(A\) is stretched, well within the elastic limit, horizontally between two pillars (figure). A mass \(m\) is suspended from the mid-point of the wire. Strain in the wire is:
    

1.	\( \dfrac{x^2}{2 L^2} \)	2.	\(\dfrac{x}{\mathrm{~L}} \)
3.	\(\dfrac{x^2}{L}\)	4.	\(\dfrac{x^2}{2L}\)

9. A rod of length \(l\) and negligible mass is suspended at its two ends by two wires of steel (wire \(A\)) and aluminium (wire \(B\)) of equal lengths (figure). The cross-sectional areas of wires \(A\) and \(B\) are \(1.0~\text{mm}^2\) and \(2.0~\text{mm}^2\) respectively.
\((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) and \(Y_{\text{steel}}=200\times10^9~\text{N/m}^2)\)
          

(a)	The mass \(m\) should be suspended close to wire \(A\) to have equal stresses in both wires.
(b)	The mass \(m\) should be suspended close to \(B\) to have equal stresses in both wires.
(c)	The mass \(m\) should be suspended in the middle of the wires to have equal stresses in both wires.
(d)	The mass \(m\) should be suspended close to wire \(A\) to have equal strain in both wires.

 
The correct statements are:

1.	(b), (c)	3.	(b), (d)
2.	(a), (d)	4.	(c), (d)

10. A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Fig. 9.1). A mass m is suspended from the mid point of the wire. Strain in the wire is

1. \(\frac{x^2}{2 L^2} \)
2. \(\frac{x}{L}\)
3. \(\frac{x^2}{L} \)
4. \(\frac{x^2}{2 L}\)