Find the ratio between the depths where the pressure are 3- 105 N m-2 and 5- 105 Nm-2-PA-105 Nm-2

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Standard XII

Physics

Pressure

Find the rati...

Question

Find the ratio between the depths where the pressure are $3 \times 10^{5} N m^{- 2}$ and $5 \times 10^{5} N m^{- 2} . (P_{A} = 10^{5} N m^{- 2})$

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Solution

let the depths be $h_{1}$ and $h_{2}$ respectively
so pressure at depth $h_{1}$ = $P_{A}$ + $ρ g h_{1}$ = $3 \times 10^{5} P a$ so $ρ g h_{1}$ = $2 \times 10^{5} P a$ ...................(1)
as $P_{A}$ = $10^{5}$ Pa

and pressure at depth $h_{2}$ = $P_{A}$ + $ρ g h_{2}$ = $5 \times 10^{5}$ Pa so $ρ g h_{2}$ = $4 \times 10^{5}$ Pa ..............(2)

now, on dividing 2nd by 1st we get $\frac{h_{2}}{h_{1}}$ = 2

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Find the ratio between the depths where the pressure are 3×105Nm−2 and 5×105Nm−2.(PA=105Nm−2)

let the depths be h1 and h2 respectivelyso pressure at depth h1 = PA + ρgh1 =3×105Pa so ρgh1 = 2×105Pa ...................(1) as PA = 105Paand pressure at depth h2= PA + ρgh2 = 5×105Pa so ρgh2 = 4×105Pa ..............(2)now, on dividing 2nd by 1st we get h2h1 = 2

Find the ratio between the depths where the pressure are $3 \times 10^{5} N m^{- 2}$ and $5 \times 10^{5} N m^{- 2} . (P_{A} = 10^{5} N m^{- 2})$