A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are

Q: A concrete sphere of radius $R$ has a cavity of radius $ r$ which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$ and $0.3$ for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

b (b)Let specific gravities of concrete and saw dust are ${\rho _1}$ and ${\rho _2}$ respectively. According to principle of floatation weight of whole sphere = upthrust on the sphere $\frac{4}{3}\pi ({R^3} - {r^3}){\rho _1}g + \frac{4}{3}\pi {r^3}{\rho _2}g = \frac{4}{3}\pi {R^3} \times 1 \times g$ ==> ${R^3}{\rho _1} - {r^3}{\rho _1} + {r^3}{\rho _2} = {R^3}$ ==> ${R^3}({\rho _1} - 1) = {r^3}({\rho _1} - {\rho _2})$ ==> $\frac{{{R^3}}}{{{r^3}}} = \frac{{{\rho _1} - {\rho _2}}}{{{\rho _1} - 1}}$ ==> $\frac{{{R^3} - {r^3}}}{{{r^3}}} = \frac{{{\rho _1} - {\rho _2} - {\rho _1} + 1}}{{{\rho _1} - 1}}$ ==> $\frac{{({R^3} - {r^3}){\rho _1}}}{{{r^3}{\rho _2}}} = \left( {\frac{{1 - {\rho _2}}}{{{\rho _1} - 1}}} \right)\;\frac{{{\rho _1}}}{{{\rho _2}}}$ ==> $\frac{{{\rm{Mass of concrete }}}}{{{\rm{Mass of saw dust}}}} = \left( {\frac{{1 - 0.3}}{{2.4 - 1}}} \right) \times \frac{{2.4}}{{0.3}} = 4$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A concrete sphere of radius $R$ has a cavity of radius $ r$ which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$ and $0.3$ for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

A$8$
B$4$
C$3$
D$0$

AIIMS 1995, Diffcult

STD 11 Science
NEET
STD 11 - 9.1. fluid mechanics
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
Two identical cylindrical vessels with their bases at same level each contains a liquid of density $\rho$. The height of the liquid in one vessel is ${h_1}$ and that in the other vessel is ${h_2}$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected, is
View Solution
2
Some liquid is filled in a cylindrical vessel of radius $R$. Let $ F_1 $ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square crss-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. Then:
View Solution
3
A cubical block of wood of specific gravity $0.5$ and a chunk of concrete of specific gravity $2.5$ are fastened together. The ratio of the mass of wood to the mass of concrete which makes the combination to float with its entire volume submerged under water is
View Solution
4
We have two (narrow) capillary tubes $T_1$ and $T_2$. Their lengths are $l_1$ and $l_2$ and radii of cross-section are $r_1$ and $r_2$ respectively. The rate of flow of water under a pressure difference $ P$ through tube $T_1$ is $8cm ^3/sec$. If $l_1 = 2l_2$ and $ r_1 =r_2$, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before $ (= P)$
View Solution
5
Two immiscible liquid are filled in conical flask as shown in figure. The area of cross section is shown, a small hole of area a is made in lower end of cone. Find speed of liquid flow from hole
View Solution
6
A liquid flows through a horizontal tube. The velocities of the liquid in the two sections which have areas of cross-section $A_1$ and $A_2$ are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$ . The incorrect statement is
View Solution
7
Two substances of densities ${\rho _1}$ and ${\rho _2}$ are mixed in equal volume and the relative density of mixture is $4$. When they are mixed in equal masses, the relative density of the mixture is $3$. The values of ${\rho _1}$ and ${\rho _2}$ are
View Solution
8
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. Tank is resting on a smooth horizontal surface. Horizontal force which will have to be applied on the tank to keep it in equilibrium is
View Solution
9
Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

$(A)$ $d_Ad_F$ $(B)$ $d_B > d_F$ $(C)$ $d_A>d_F$ $(D)$ $d_A+d_B=2 d_F$
View Solution
10
Two capillary tubes of same radius $r$ but of lengths $l_1$ and $l_2$ are fitted in parallel to the bottom of a vessel. The pressure head is $P$. What should be the length of a single tube that can replace the two tubes so that the rate of flow is same as before
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free