Question

A student plots a graph from his readings on the determination of Young's modulus of a metal wire but forgets to put the labels (figure 14-Q4). The quantities on X and Y-axes may be respectively

(a) weight hung and length increased
(b) stress applied and length increased
(c) stress applied and strain developed
(d) length increased and the weight hung.

Answer 1

All are correct

Explanation: 

It is clear from the graph that the quantity along one axis is directly proportional to the quantity along another axis. We know that stress/strain = Y (constant) 

→W/A = Y*l/L 

→W =(YA/L)*l 

For a given wire, cross-sectional area A and the length L is constant. 

Hence  

W = K*l {where YA/L =K, a constant} 

→W∝l 

i.e. the weight hung is proportional to the length increased. So the option (a) is true.  

If we write the expression as W/A = (Y/L)*l 

→stress ∝ length increased {where Y/L is another constant} 

Hence the option (b) is true.  

Since the stress is directly proportional to the strain developed and the constant of proportionality is Young's modulus of elasticity. Hence the option (c) is correct.  

It is the same case of option (a) simply the axes have been changed. Which is also true. Hence the option (d) is true.  

Thus all options are true.