The average depth of the Indian Ocean is about \(3000\) 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 \(2.2\times10^{9}\) Nm^-2 and \(g=10\) ms^-2)
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)

The edge of an aluminium cube is \(10\) cm long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100\) kg is then attached to the opposite face of the cube. The shear modulus of aluminium is \(25\) GPa. What is the vertical deflection of this face?
1. \(4.86 \times10^{-6}\) m
2. \(3.92 \times 10^{-7}\) m
3. \(3.01 \times10^{-6}\) m
4. \(6.36 \times10^{-7}\) m

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

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. \(\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.

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,

A mild steel wire of length \(\mathrm{2L}\) 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. \( \frac{x^2}{2 L^2} \)
2. \(\frac{x}{\mathrm{~L}} \)
3. \(\frac{x^2}{L}\)
4. \(\frac{x^2}{2L}\)

The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:

The modulus of rigidity of the ideal liquid is: