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When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, then the increase in length will be -
(1) 0.5 cm                             
(2) 2 cm
(3) 4 cm                                 
(4) 8 cm

A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be:

A and B are two wires of same material. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is
(1) Equal to that on A
(2) Four times that on A
(3) Two times that on A               
(4) Half that on A

Two wires of copper having length in the ratio of \(4:1\) and radii ratio of \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two will be:

There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is
(1)   + 0.50                               
(2)   – 0.50
(3)   0.25                                  
(4)   – 0.25

A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire by a constant force F is proportional to:
(1) $\frac{1}{L^2}$                                             
(2) $\frac{1}{L}$
(3) $L^2$                                               
(4) L

The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is
(1) a - b                                             
(2) 5b - 4a
(3) 2b -$\frac{1}{4}\mathrm{a}$                                       
(4) 4a - 3b

If a rubber ball is taken at the depth of 200 m in a pool, its volume decreases by 0.1%. If the density of the water is $1\times {10}^{3}kg/m^3$ and $g=10m/s^2$, then the volume elasticity in  will be
(1) ${10}^8$                                       
(2) $2\times {10}^8$
(3)${10}^9$                                         
(4) $2\times {10}^9$

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is  $\beta$ and the coefficient of volume expansion is $\alpha$ -
(1) $\frac{P}{\alpha \beta }$                                 
(2) $\frac{P\alpha }{\beta }$
(3) $\frac{P\beta }{\alpha }$                                 
(4) $\frac{\alpha \beta }{P}$
 

Two wires A and B of same length and of the same material have the respective radii $r_1$ and $r_2$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be
(a) $\frac{r_1^2}{r_2^2}$                                           (b) $\frac{r_2^2}{r_1^2}$
(c) $\frac{r_2^4}{r_1^4}$                                           (d) $\frac{r_1^4}{r_2^4}$

A cube of aluminium of sides \(0.1~\text{m}\) is subjected to a shearing force of \(100\) N. The top face of the cube is displaced through \(0.02\) cm with respect to the bottom face. The shearing strain would be:
1. \(0.02\)                                   
2. \(0.1\)
3. \(0.005\)                               
4. \(0.002\)

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) $8\theta /9$

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

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

Two wires of the same diameter of the same material having the length \(l\) and \(2l.\) If the force \(F\) is applied on each, the ratio of the work done in the two wires will be:
1. \(1 : 2       \)
2. \(1 : 4\)
3. \(2 : 1           \)
4. \(1 : 1\)