The extension of a wire by the application of load is 3 mm. The extension in a wire of the same material and length but half the radius by the same load is -

(1) 12 mm                                 

(2) 0.75 mm

(3) 15 mm

(4) 6 mm

The isothermal elasticity of a gas is equal to

(1) Density                                     

(2) Volume

(3) Pressure                                    

(4) Specific heat

The adiabatic elasticity of a gas is equal to
1. γ × density
2. γ × volume
3. γ × pressure
4. γ × specific heat

The compressibility of water is $4\times {10}^{-5}$ per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be -

(a) 0.4 cc           (b) $4\times {10}^{-5}cc$

(c) 0.025 cc       (d) 0.004 cc 

When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces by 0.01%. The bulk modulus of the material of the rubber in $dyne / c{m}^2$ is:

(1) $10\times {10}^{12}$                               

(2) $100\times {10}^{12}$

(3) $1\times {10}^{12}$                                 

(4) $20\times {10}^{12}$

When a spiral spring is stretched by suspending a load on it, the strain produced is called:

If the Young's modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be

(a) Zero                              (b) Infinity

(c) $2\times {10}^{10}N/m^2$           (d) $3\times {10}^{10}N/m^2$

One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(S\) is the area of cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W_1}{S}\)
2. \(\frac{W_1+\left(\frac{W}{4}\right)}{S}\)
3. \(\frac{W_1+\left(\frac{3W}{4}\right)}{S}\)
4. \(\frac{W_1+W}{S}\)

The diagram shows a force-extension graph for a rubber band. Consider the following statements

I. It will be easier to compress this rubber than expand it

II. Rubber does not return to its original length after it is stretched

III. The rubber band will get heated if it is stretched and released

 Which of these can be deduced from the graph?

(1)   III only                              

(2)   II and III

(3)   I and III                            

(4)   I only

The adjacent graph shows the extension $\left(∆l\right)$ of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is ${10}^{-6}{m}^2$ calculate the young’s modulus of the material of the wire

(a) $2\times {10}^{11}N/m^2$

(b) $2\times {10}^{-11}N/m^2$

(c) $3\times {10}^{-12}N/m^2$

(d) $2\times {10}^{-13}N/m^2$