A rod of length l and radius r is joined to a rod of length l/2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $\theta$, the twist angle at the joint will be 

(a) $\theta /4$                          (b) $\theta /2$

(c) $5\theta /6$                         (d) $8\theta /9$

Shearing stress causes a change in-

(1)   Length                              

(2)   Breadth

(3)   Shape                               

(4)   Volume

To break a wire, a force of ${10}^{6}N/m^2$ is required. If the density of the material is $3\times {10}^3 kg/m^3$, then the length of the wire which will break by its own weight will be -

(a) 34 m                             (b) 30 m

(c) 300 m                            (d) 3 m

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 strain-stress curves of three wires of different materials are shown in the figure. \(P\), \(Q\) and \(R\) are the elastic limits of the wires. The figure shows that:
           

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) $2\times {10}^{-13}N/m^2$

The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook’s law. \(P\) and \(Q\) represents:

             
1. \(P\) = applied force, \(Q\) = extension
2. \(P\) = extension, \(Q\) = applied force
3. \(P\) = extension, \(Q\) = stored elastic energy
4. \(P\) = stored elastic energy, \(Q\) = extension 

The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that

(1) A is brittle but B is ductile  

(2) A is ductile and B is brittle

(3) Both A and B are ductile      

(4) Both A and B are brittle

If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

(1) V/25                                   

(2) 5V

(3) V/5                                    

(4) 25V