A hollow sphere of volume $V$ is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water
A hollow sphere of volume $V$ is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water
- A
$V/2$
- B
$V/3$
- C
$V/4$
- D
$V$
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Karman line is a theoretical construct that separates the earth's atmosphere from outer space. It is defined to be the height at which the lift on an aircraft flying at the speed of a polar satellite $(8 \,km / s )$ is equal to its weight. Taking a fighter aircraft of wing area $30 \,m ^2$, and mass $7500 \,kg$, the height of the Karman line above the ground will be in the range .............. $km$ (assume the density of air at height $h$ above ground to be $\rho( h )=1.2 e ^{\frac{ h }{10}} \,kg / m ^3$ where $h$ is in $km$ and the lift force to be $\frac{1}{2} \rho v^2 A$, where $v$ is the speed of the aircraft and $A$ its wing area).
Karman line is a theoretical construct that separates the earth's atmosphere from outer space. It is defined to be the height at which the lift on an aircraft flying at the speed of a polar satellite $(8 \,km / s )$ is equal to its weight. Taking a fighter aircraft of wing area $30 \,m ^2$, and mass $7500 \,kg$, the height of the Karman line above the ground will be in the range .............. $km$ (assume the density of air at height $h$ above ground to be $\rho( h )=1.2 e ^{\frac{ h }{10}} \,kg / m ^3$ where $h$ is in $km$ and the lift force to be $\frac{1}{2} \rho v^2 A$, where $v$ is the speed of the aircraft and $A$ its wing area).
- [KVPY 2021]
A jar is filled with two non-mixing liquids $1$ and $2$ having densities $\rho_1$ and, $\rho_2$ respectively. A solid ball, made of a material of density $\rho_3$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for $\rho_1 , \rho_2$ and $\rho_3$?
A jar is filled with two non-mixing liquids $1$ and $2$ having densities $\rho_1$ and, $\rho_2$ respectively. A solid ball, made of a material of density $\rho_3$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for $\rho_1 , \rho_2$ and $\rho_3$?
- [AIEEE 2008]
A cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is $g$, the spring constant of the spring is:
A cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is $g$, the spring constant of the spring is: