First slide

Pressure in a fluid-mechanical properties of fluids

Question

A streamlined body falls through air from a height h on the surface of a liquid. If d and D(D > d) represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is

Moderate

A

$\sqrt{\frac{2 h}{g}}$
B

$\sqrt{\frac{2 h}{g} \cdot \frac{D}{d}}$
C

$\sqrt{\frac{2 h}{g} \cdot \frac{d}{D}}$
D

$\sqrt{\frac{2 h}{g}} (\frac{d}{D - d})$

Solution

$Upthrust - weight of body = apparent weight$
$V D g - V d g = V d a$
where a = retardation of body
$∴ a = (\frac{D - d}{d}) g$
The velocity gained after fall from h height in air, $v = \sqrt{2 g h}$
Hence, time to come in rest,
$t = \frac{v}{a} = \frac{\sqrt{2 g h} \times d}{(D - d) g} = \sqrt{\frac{2 h}{g}} \times \frac{d}{(D - d)}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App