A body of density rho is dropped from rest fr | vedclass

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

Question

(C) Let $V$ be the volume of the body. When the body is dropped from height $h$,its velocity $v$ just before entering the water is given by $v = \sqrt

Vedclass · Accepted Answer

$\frac{h \rho}{\sigma-\rho}$

Vedclass · Answer

(C) Let $V$ be the volume of the body. When the body is dropped from height $h$,its velocity $v$ just before entering the water is given by $v = \sqrt{2gh}$.As the body sinks to a maximum depth $h'$,its final velocity becomes zero. We can apply the work-energy theorem: the work done by gravity plus the work done by the buoyant force equals the change in kinetic energy.Work done by gravity = $(mg)h' = (V \rho g)h'$Work done by buoyant force = $-(F_B)h' = -(V \sigma g)h'$Change in kinetic energy = $K_f - K_i = 0 - \frac{1}{2}mv^2 = -\frac{1}{2}(V \rho)(2gh) = -V \rho gh$Equating the work done to the change in kinetic energy:$(V \rho g)h' - (V \sigma g)h' = -V \rho gh$$V g h' (\rho - \sigma) = -V \rho gh$$h' (\sigma - \rho) = h \rho$$h' = \frac{h \rho}{\sigma - \rho}$

$A$ body of density $\rho$ is dropped from rest from a height $h$ into a lake of density $\sigma$,where $\sigma > \rho$. Neglecting all dissipative forces,the maximum depth to which the body sinks before returning to float on the surface is:

Similar Questions

State the law of floatation.

$A$ block of wood of volume $V$ floats in water with half of its volume submerged. The same block floats in an oil with $0.8 \,V$ volume submerged. If the density of water is $1000 \,kg \,m^{-3}$, then the density of the oil is

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with an acceleration of $g/3$, the fraction of volume immersed in the liquid will be

$A$ cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma$ $(< \rho)$ until it is fully immersed. The increase in pressure at the bottom of the vessel is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module