Water and oil are taken in two separate beakers, the density of water is $1000 k g / m^{3}$ and the density of oil is $1500 k g / m^{3}$ . At what depth, the pressure in oil beaker will be the same as the pressure at $150 c m$ in the water beaker? (Acceleration due to gravity = $10 m / s^{2}$ )

$150 c m$

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$50 c m$

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$75 c m$

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$100 c m$

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Solution

The correct option is D
$100 c m$

Given,

Density of water, $ρ_{w} = 1000 k g / m^{3}$

Density of oil, $ρ_{o} = 1500 k g / m^{3}$

Acceleration due to gravity, $g$ = $10 m / s^{2}$

Pressure at a depth h, $P = h \times ρ \times g$

let the depth at which the pressure in oil is same as in water at $150 c m$ be $Y$ .

The pressure in water at $150 c m$ = The pressure in oil at $Y c m$ .

$⟹ 150 \times 1000 \times g = Y \times 1500 \times g$

$⟹ 150 \times 1000 = Y \times 1500$

$⟹ Y = \frac{150 \times 1000}{1500}$

$Y = 100 c m$ .

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Water and oil are taken in two separate beakers, the density of water is 1000 kg/m $^{3}$ and the density of oil is 1500 kg/m $^{3}$ . At what depth, the pressure in oil beaker will be the same as the pressure at 150 cm depth, in the water beaker ?

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Water and oil are taken in two separate beakers, the density of water is 1000 kg/m3 and the density of oil is 1500 kg/m3. At what depth, the pressure in oil beaker will be the same as the pressure at 150 cm in the water beaker? (Acceleration due to gravity = 10 m/s2)

Water and oil are taken in two separate beakers, the density of water is $1000 k g / m^{3}$ and the density of oil is $1500 k g / m^{3}$ . At what depth, the pressure in oil beaker will be the same as the pressure at $150 c m$ in the water beaker? (Acceleration due to gravity = $10 m / s^{2}$ )