A fluid container is containing a liquid of density $\rho $ is accelerating upward with acceleration a along the inclined place of inclination $\alpha$ as shown. Then the angle of inclination $ \theta $ of free surface is :
${\tan ^{ - 1}}\left[ {\frac{a}{{g\cos \alpha }}} \right]$
${\tan ^{ - 1}}\left[ {\frac{{a + g\sin \alpha }}{{g\cos \alpha }}} \right]$
${\tan ^{ - 1}}\left[ {\frac{{a - g\sin \alpha }}{{g(1 + \cos \alpha )}}} \right]$
${\tan ^{ - 1}}\left[ {\frac{{a - g\sin \alpha }}{{g(1 - \cos \alpha )}}} \right]$
A metal ball of density $7800\ kg/m^3$ is suspected to have a large number of cavities . It weighs $9.8$ $kg$ when weighed directly on a balance and $1.5$ $kg$ less when immersed in water . The fraction by volume of the cavities in the metal ball is approximately ....... $\%$
A cubical block of wood of edge $10$ $cm$ and mass $0.92$ $kg$ floats on a tank of water with oil of rel. density $0.6$ to a depth of $4$ $cm$ above water. When the block attains equilibrium with four of its sides edges vertical
There is a metal cube inside a block of ice which is floating on the surface of water. The ice melts completely and metal falls in the water. Water level in the container
A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance $l $ and $h$ are shown there. After some time the coin falls into the water. Then
A silver ingot weighing $2.1 kg$ is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of silver is $10.5$ . The tension in the string in $kg-wt$ is