Water flows out of the hole on the side of a bucket and follows a parabolic path. If the bucket falls freely under gravity, ignoring air resistance, the water flow
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A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is
A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000\; kg$. The area of cross-section of the piston carrying the load is $425 \;cm ^{2} .$ What maximum pressure would the smaller piston have to bear?
A tank $5 \,m$ high is half filled with water and then is filled to the top with oil of density $0.85 \,g/cm^3$. The pressure at the bottom of the tank, due to these liquids is ........ $g/cm^2$
The area of cross-section of a large tank is $0.5 \; m ^{2}$. It has a narrow opening near the bottom having area of cross-section $1 \; cm ^{2}$. A load of $25 \; kg$ is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $40 \; cm$ above the bottom, will be $\dots \; cms ^{-1}$. $\left[\right.$ Take $\left.g =10 \; ms ^{-2}\right]$
A vertical cylindrical container of base area $A$ and upper cross-section area $A_1$ making an angle $30^o $ with the horizontal is placed in an open rainy field as shown near another cylindrical container having same base area $A$. The ratio of rates of collection of water in the two containers will be
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).