Question

"If the end of the crutch is a circle of radius 1.2 cm without the tip, and the rubber tip is a circle of radius 2.3 cm , by what factor does the tip reduce the pressure exerted by the crutch?"

Answer 1

Answer:

The pressure exerted by the crutch is reduced factor by 0.72.

Explanation:

Given that,

Radius of crutch = 1.2 cm

Radius of tip = 2.3 cm

We need to calculate the pressure without tip

Using formula of pressure

$P=\dfrac{F}{A}$

$P_{1}=\dfrac{F}{\pi r^2}$

Put the value into the formula

$P_{1}=\dfrac{F}{\pi\times(1.2\times10^{-2})^2}$....(I)

We need to calculate the pressure with tip

Using formula of pressure

$P_{2}=\dfrac{F}{\pi r^2}$

$P_{2}=\dfrac{F}{\pi\times(2.3\times10^{-2})^2}$....(II)

We need to calculate the reduction factor

Using formula of reduction factor

$\text{reduction factor}=\dfrac{P_{1}-P_{2}}{P_{1}}$

Put the value into the formula

$\text{reduction factor}=\dfrac{\dfrac{F}{\pi\times(1.2\times10^{-2})^2}-\dfrac{F}{\pi\times(2.3\times10^{-2})^2}}{\dfrac{F}{\pi\times(1.2\times10^{-2})^2}}$

Here, F is the same

$\text{reduction factor}=\dfrac{\dfrac{1}{(1.2\times10^{-2})^2}-\dfrac{1}{(2.3\times10^{-2})^2}}{\dfrac{1}{(1.2\times10^{-2})^2}}$

$\text{reduction factor}=0.72$

The pressure exerted by the crutch is reduced by 72%.

Hence, The pressure exerted by the crutch is reduced factor by 0.72.