Question

If two forces in the ratio 3:4 act on two areas in the ratio 4:5, Find the ratio of pressure exerted?

Answer 1

Answer:

Let the common factor in ratio of the forces be $x$

Then forces are $3x,4x$

Let the common factor in ratio of the areas be $y$

Then areas are $4y, 5y$

We know that pressure = force ÷ area

= So pressure of object having $3x$ force = force ÷ area

= $3x$ ÷ $4y$

Pressure of object having $4x$ force = force ÷ area

=  $4x$ ÷ $5y$

Ratio of both pressures = pressure of object having $3x$ force  ÷ pressure of object having $4x$ force  

= ($3x$ ÷ $4y$ ) ÷ ($4x$ ÷ $5y$)

= $3x$ ÷ $4y$ × $5y$ ÷ $4x$

= $15xy$ ÷ $16xy$

Cut $xy$ as it is in both terms

So we get ratio as 15 : 16

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Answer 2

Answer:

the answer is 15:16