Question

A hammer exerts a force of 1.5kgf on 2 nails a and b. If the pressure experienced by the nails are in ratio 1:3 find the ratio of their areas of cross sections

Answer 1

Given that, the pressure experienced by the nails are in ratio 1:3.

Also, a hammer exerts a force of 1.5kgf on two nails; A and B.

Let us assume that the pressure exerted by nail A is 1M and the pressure exerted by nail B is 3M.

Now,

Pressure = Force/Area

For nail A:

1M = 1.5/(Area of nail A)

Area of nail A = 1.5/1M

For nail B:

3M = 1.5/(Area of nail B)

Area of nail B = 1.5/3M

We have to find the ratio of their areas of cross-sections.

Therefore,

(Area of nail A)/(Area of nail B) = (1.5/1M)/(1.5/3M)

(Area of nail A)/(Area of nail B) = 1.5/1M × 3M/1.5

(Area of nail A)/(Area of nail B) = 3M/1M

(Area of nail A)/(Area of nail B) = 3/1

→ Area of nail A : Area of nail B = 3:1

OR

→ Area of a cross-section of nail A : Area of a cross-section of nail B = 3:1.

Answer 2

Given :-

• A hammer exerts a force of 1.5 kgf on 2 nails, A and B.

• The pressure experienced by the nails are in ratio of 1:3.

To find :-

The ratio of their areas of cross sections.

Solution :-

Let the pressure exerted on nail A be 1P and the pressure exerted on nail B be 3P.

Now,

$\bold{\longrightarrow}$ For nail A,

Pressure = Force/Area

⇒1P = 1.5/A

⇒Area of nail A(A) = 1.5/1P

$\bold{\longrightarrow}$ For nail B,

Pressure = Force/Area

⇒3P = 1.5/A'

⇒Area of nail B(A') = 1.5/3P

Now, ratio of their areas:

$\displaystyle{\sf{\frac{A}{A'}=\frac{\frac{1.5}{1P} }{\frac{1.5}{3P} } }}\\\\\\\displaystyle{\sf{\implies \frac{A}{A'}=\frac{3P}{1P} }}\\\\\\\displaystyle{\sf{\implies \frac{A}{A'}=\frac{3}{1} }}$

So, A : A' = 3 : 1

∴Or, Area of cross section of nail A : Area of cross section of nail B = 3 : 1.