A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4\,h$ from the surface of water in a water tank kept on a horizontal surface. If $l << h,\,r << h$ and the rate of water flow from the holes is the same, then $r$ is equal to

823-904

  • A

    $\frac{l}{{\sqrt {2\pi } }}$

  • B

    $\frac{l}{{\sqrt {3\pi } }}$

  • C

    $\frac{l}{{{3\pi } }}$

  • D

    $\frac{l}{{{2\pi } }}$

Similar Questions

A wind with speed $40\,m/s$ blows parallel to the roof of a house. The area of the roof is $250\,m^2.$ Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $(\rho _{air} = 1.2\,kg/m^3)$

A manometer reads the pressure of a gas in an enclosure as shown in the figure.

The absolute and gauge pressure of the gas in $cm$ of mercury is
(Take atmospheric pressure $= 76\,cm$ of mercury)

A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. The terminal speed of the ball is

A candle of diameter $d$ is floating on a liquid in a cylindrical container of diameter $D\left( {D >  > d} \right)$ as shown in figure. If it is burning at the rate of $2\  cm/hour$ then the top of the candle will

A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next?