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
$g\, h\, \rho a$
$\frac{2gh}{\rho a}$
$2g\, h\, \rho a$
$\frac{\rho gh}{a}$
The weight of an empty balloon on a spring balance is $w_1$. The weight becomes $w_2$ when the balloon is filled with air. Let the weight of the air itself be $w$ .Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside $\&$ outside the balloon. Then :
A metallic sphere weighing $3 \,kg$ in air is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of metallic is $10$. The tension in the string is ........ $N$
Construction of submarines is based on
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A:$ When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.
Reason $R:$ A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements, choose the most appropriate answer from the options given below
An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was