A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P ( r )$ is the pressure at $r ( r < R )$, then the correct option$(s)$ is(are)
$(A)$ $P ( I =0)=0$ $(B)$ $\frac{ P ( r =3 R / 4)}{ P ( r =2 R / 3)}=\frac{63}{80}$
$(C)$ $\frac{ P ( r =3 R / 5)}{ P ( r =2 R / 5)}=\frac{16}{21}$ $(D)$ $\frac{ P ( r = R / 2)}{ P ( r = R / 3)}=\frac{20}{27}$
IIT 2015, Medium
Download our app for free and get started
$P(r)=K\left(1-\frac{r^2}{R^2}\right)$
Download our appand 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.*
Similar Questions
- 1A liquid having coefficient of viscosity $0.02$ decapoise is filled in a container of cross-sectional area $20 \,m ^2$. If viscous drag between two adjacent layers in flowing is $1 \,N$, then velocity gradient is ........ $s ^{-1}$View Solution
- 2A small spherical ball of radius $0.1 \,mm$ and density $10^{4} \,kg m ^{-3}$ falls freely under gravity through a a distance $h$ before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $h$ wil be $m$. (Given $g =10 \,ms ^{-2}$, viscosity of water $=1.0 \times 10^{-5} \,N - sm ^{-2}$ )View Solution
- 3In a cylindrical container open to the atmosphere from the top a liquid is filled upto $10\,\, m$ depth. Density of the liquid varies with depth from the surface as $\rho (h) = 100 + 6h^2$ where $h$ is in meter and $\rho$ is in $kg/m^3.$ The pressure at the bottom of the container will be : $($ atmosphere pressure $= 10^5\,\, Pa, \,g = 10\, m/sec^2)$View Solution
- 4A rectangular box has water in it. It is being pulled to the right with an acceleration $a$. Which of the following options shows the correct shape of water surface on it ?View Solution
- 5A rectangular block is $10 \,cm \times 10 \,cm \times 15 \,cm$ in size is floating in water with $10 \,cm$ side vertical. If it floats with $15 \,cm$ side vertical, then the level of water will ..........View Solution
- 6The bulk modulus of a liquid is $3 \times 10^{10}\, Nm ^{-2}$. The pressure required to reduce the volume of liquid by $2 \%$ is ........ $\times 10^{8}\; Nm ^{-2}$View Solution
- 7The value of $g $ at a place decreases by $ 2\%.$ The barometric height of mercuryView Solution
- 8The top of a water tank is open to air and its water level is maintained. It is giving out $0.74\,m^3$ water per minute through a circular opening of $2\,cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ $m$View Solution
- 9A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area $'a'$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is $(a\,<\,<\,A)$View Solution
- 10A capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by $10\%$ then the rate of flow of liquid will change nearly by ......... $\%$View Solution