Question

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

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Answer 1

Let F/a be the pressure experienced by nail A, where a is the area. and F/b be the same for B.

F/a : F/b = 1 : 3

1/a : 1/b = 1 : 3

1/a = 1/3

1/b

b/a = 1/3

a/b = 3/1

a : b = 3 : 1

Answer 2

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

$\bold{force \: = \: 1.5N} \\ \bold{area \: = \: 2m {m}^{2} \: to \: {m}^{2} } \\ \bold{1m{m}^{2} \: = \: 1mm \: \times 1mm} \\ \bold{ \: \: \: = 0.001m \times 0.001m} \\ \bold{ \: \: \: = 1 \times {10}^{ - 6} {m}^{2} }$

$\bold{\: Pressure \: on \: nail \: A \: = \: \frac{force}{area} } \\ \bold{ \: \: \: \: \: \: \: \: \: = \frac{1.5}{2 \times 1 \times {10}^{ - 6} } } \\ \bold{ \: \: \: = \frac{ \cancel{1.5} \: \: ³}{2 \times 1 \times {10}^{ - 6} \times \cancel{10} \: \: ²} } \\ \\ \bold{ \: \: \: = \: 7.5 \times {10}^{5}Pa \: \: \: ...ans}$

$\bold{Pressure \: on \: nail \: B \: = \frac{force}{area} } \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \frac{1.5}{6 \times 1 \times {10}^{ - 6} } } \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \frac { \cancel{1.5} \: \: ³}{ \cancel6 \:² \times 1 \times {10}^{ - 6} \times \cancel{10}\: ² } } \\ \bold{ = \: 2.5 \times {10}^{5}Pa \: \: \: ....ans}$

hope it helps you...

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