Correct Answer - Option 3 : 1

**Concept:**

**Punching:**

in sheet metal operation, punching operation the process in which sheared part is considered as scrap and the remaining part is desired part.

**For punching opreration,**

⇒ Punch tool size = Hole size = d

The maximum crushing stress induced in the punching tool,

**\( ⇒ {{\bf{\sigma }}_{{\bf{cmax}}}} = \frac{{4{\bf{F}}}}{{{\bf{\pi }}{{\bf{d}}^2}}}\;\;\;\;\; \ldots \left( 1 \right)\;\)**

The maximum allowable shearing stress,

\( ⇒ {{\bf{\tau }}_{{\bf{smax}}}} = \frac{{\bf{F}}}{{{\bf{\pi dt}}}}\;\;\;\;\;\; \ldots \left( 2 \right)\;\)

where, F = Punching force, d = diameter of the hole (punching tool diameter), t = thickness of the metal sheet

**Calculation:**

**Given:**

**σ**_{cmax} = 4τ_{smax}

**\( ⇒ \frac{{4{\bf{F}}}}{{{\bf{\pi }}{{\bf{d}}^2}}} = 4 \times \frac{{\bf{F}}}{{{\bf{\pi dt}}}}\;\)**

**⇒ d = t**

**⇒ The ratio of the diameter of the hole to plate thickness = 1**