A streamlined body falls through air from a h | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $V$ be the volume of the body. The velocity of the body just before entering the liquid is $v = \sqrt{2gh}$.When the body enters the liquid,th

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Let $V$ be the volume of the body. The velocity of the body just before entering the liquid is $v = \sqrt{2gh}$.When the body enters the liquid,the forces acting on it are its weight $W = Vdg$ (downwards) and the buoyant force $F_B = VDg$ (upwards).The net force $F_{net}$ acting on the body inside the liquid is $F_B - W = VDg - Vdg = V(D - d)g$.The retardation $a$ of the body is given by $a = \frac{F_{net}}{m} = \frac{V(D - d)g}{Vd} = \left( \frac{D - d}{d} \right)g$.The body comes to rest when its velocity becomes zero. Using $v = at$,we get $t = \frac{v}{a}$.Substituting the values,$t = \frac{\sqrt{2gh}}{\left( \frac{D - d}{d} \right)g} = \frac{\sqrt{2gh}}{g} \cdot \frac{d}{D - d} = \sqrt{\frac{2h}{g}} \cdot \frac{d}{D - d}$.

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

Similar Questions

An aluminium sphere is dipped into water. Which of the following is true?

The weight of a sphere in air is $50 \ g$. Its weight is $40 \ g$ in a liquid at temperature $20^{\circ} C$. When the temperature increases to $70^{\circ} C$,its weight becomes $45 \ g$. The ratio of the densities of the liquid at the two given temperatures is: (in $: 1$)

$A$ pendulum has a time period $T$ in air. When it is made to oscillate in water,it acquires a time period $T' = \sqrt{2} T$. The density of the pendulum bob is (density of water $= 1$)

State and prove Archimedes' principle.

$A$ ball of relative density $0.8$ falls into water from a height of $2 \ m$. The depth to which the ball will sink is ........ $m$ (neglect viscous forces):

Vedclass Test Series

Exam Paper Generator

Online Exam Module