A vessel contain a liquid has a constant acceleration $19.6 \,m / s ^2$ in horizontal direction. The free surface of water get sloped with horizontal at angle ..........
$\tan ^{-1}\left[\frac{1}{2}\right]$
$\sin ^{-1}\left[\frac{1}{\sqrt{3}}\right]$
$\tan ^{-1}[\sqrt{2}]$
$\sin ^{-1}\left[\frac{2}{\sqrt{5}}\right]$
A block of ice floats on a liquid of density $1.2$ in a beaker then level of liquid when ice completely melt
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).
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 sphere of solid material of relative density $9$ has a concentric spherical cavity and floats having just sinked in water. If the radius of the sphere be $R$, then the radius of the cavity $(r)$ will be related to $R$ as :-
A boy has $60\, kg$ weight. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$, what is the minimum volume of wooden log? (density of river water is $1000\, kg/m^3$)