Question

The stress induced in a body, when suddenly loaded, is __________ the stress-induced when the same load is applied gradually.

• A. Twice
• B. Equal to
• C. One-half
• D. Four times

Answer 1

The correct option is A

Twice

The explanation for the correct option:

In the case of option A,

1. The stress created whenever a load is delivered quickly is double that induced whenever a load is applied gradually.
2. The greatest deflection or deformation produced in material whenever a force is applied instantaneously is double the deflection or deformation induced throughout material whenever a load is employed gradually.
3. This same strain storing energy in material whenever a load is applied unexpectedly is $4$ times the strain energy that is stored in substance whenever a load is applied progressively.

Mathematical representation:

1. When the load is loaded gradually: When the maximum load P is attained, the internal force will be in equilibrium with the external force
   $$\begin{gathered} \mathrm{F}=\mathrm{kx}=\mathrm{P}\mathrm{were}\mathrm{x}\mathrm{is}\mathrm{streched}\mathrm{distance} \\ \Rightarrow \mathrm{x}=\mathrm{P}/\mathrm{k} \end{gathered}$$
2. For extending beyond the point x$x$, the internal force will be more than P and hence the particles will undergo retarded motion and ultimately will come to a stop.
3. The maximum extension as mentioned can be obtained using the work-energy equation, energy stored in the bar is equal to the work done by force.
4. As soon as the bar stops moving (extending) all the stored energy will be in the form of strain energy.
5. $\frac{1}{2}k{(x\prime )}^2=Px\prime$
   We can cancel the values and maintain $$x^{\prime }={\displaystyle \frac{2P}{k}}$$
   From the first case, we can see that $$x={\displaystyle \frac{P}{k}}$$
   That means,$x\prime =2x$

$\left(\mathrm{stress}\right)\mathrm{suddenly}=2\times \left(\mathrm{stress}\right)\mathrm{gradually}$

Therefore, the correct option is (A) twice.