A steel cable with a radius of \(1.5~\text{cm}\) supports a chairlift at a ski area. If the maximum stress is not to exceed \(10^{8}~\text{N/m}^2,\) what is the maximum load that the cable can support?
1. \(7.06\times 10^{4}~\text{N}\)
2. \(5.03\times 10^{4}~\text{N}\)
3. \(1.09\times 10^{4}~\text{N}\)
4. \(17\times 10^{4}~\text{N}\)

The volume contraction of a solid copper cube, \(10~\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7.0\times10^6~\text{Pa}\) is:
(Bulk modulus of copper is \(140 \times10^{9}~\text{Pa}.\))
1. \( 3.1 \times 10^{-2} ~\text{m}^3 \)
2. \(9.1 \times 10^{-3} ~\text{cm}^3 \)
3. \(5.0 \times 10^{-2} ~\text{cm}^3 \)
4. \(7.9 \times 10^{-2} ~\text{cm}^3 \)$$

Hooke's law is applicable for:

If two different types of rubber are found to have stress-strain curves as shown, then:
                   

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

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)

On withdrawing the external applied force on bodies within the elastic limit, the body:

The stress versus strain graph is shown for two wires. If \(Y_1\) and \(Y_2\) are Young modulus of wire \(A\) and \(B\) respectively, then the correct option is:

The breaking stress of a wire going over a smooth pulley in the following question is \(2\times 10^{9}~\text{N/m}^2.\) What would be the minimum radius of the wire used if it is not to break?