Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is  Δl. Which of the following graphs is a straight line?

(1) Δl versues 1/l

(2) Δl versus l²

(3) Δl versus 1/l²

(4) Δl versus l

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

If the length of a wire is reduced to half, then it can hold the ......... load

(1) Half                                 

(2) Same

(3) Double                             

(4) One fourth

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:

The force constant of a wire does not depend on

(1) Nature of the material                     

(2) Radius of the wire

(3) Length of the wire                           

(4) None of the above

In steel, the Young's modulus and the strain at the breaking point are $2\times {10}^{11}N{m}^{-2}$ and 0.15 respectively. The stress at the breaking point for steel is therefore -

(1) $1.33\times {10}^{11}N{m}^{-2}$           

(2) $1.33\times {10}^{12}N{m}^{-2}$

(3) $7.5\times {10}^{-13}N{m}^{-2}$           

(4) $3\times {10}^{10}N{m}^{-2}$

Which one of the following quantities does not have the unit of force per unit area?

1. Stress                                      

2. Strain

3. Young's modulus of elasticity

4. Pressure

How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm ?

(Young’s modulus for brass = $0.9\times {10}^{11}N/m^2$)

(a) Nearly 17 N                        (b) Nearly 34 N

(c) Nearly 51 N                        (d) Nearly 68 N