Question

An equal force of 100 N is applied upon two similar sharp nails at different angles as shown in figure ⇒

What will be the ratio of pressures at the tip of the nail in figure(I) and figure(II)?

• A. 1 : 1
• B. 2 : √3
• C. √3 : 2
• D. 2 : 1

Answer 1

The correct option is B

2 : √3

Only normal component of force will be responsible to drive the nail right through the wall. Also, the areas at the tip of the nails are equal as they are similar nails.

Let, $A$ be the area of tip of the nail. $P_1$ and $P_2$ be the pressures in figures (I) and (II) respectively.

Figure (I): the normal component of force $F_1$ is the total applied force $F_1=F$.

Figure (II): the normal component of force $F_2$ is $Fcos{30}^{\circ }$ i.e. $F_2=Fcos{30}^{\circ }$.

$\Rightarrow \frac{P_1}{P_2}=\frac{F_1/A}{F_2/A}=\frac{F}{Fcos{30}^{\circ }}=\frac{2}{\sqrt{3}}$