Answer

Verified

53.1k+ views

**Hint:**When an incompressible fluid flows steadily, the sum of pressure energy, kinetic energy and potential energy per unit volume of the fluid remains constant. Range is the distance covered by the projectile horizontally. Use the above statements to find the horizontal range.

**Formula used:**

${P_{atm}} + \rho gH + \dfrac{1}{2}\rho {V^2} = $Constant

Where ${P_{atm}}$ is the pressure, $g$ is the acceleration due to gravity,$\rho $ is the density

**Complete step by step answer:**

A body projected in air at an angle other than ninety degrees is called projectile. Time of flight is the time taken by body to reach the projection.

Range is the distance covered by the projectile horizontally.

The vertical displacement during time of ascent is the maximum height. In common assumptions air resistance and friction are neglected.

The energy possessed by a body due its motion is termed as Kinetic energy.

It is determined that the body can do work against a restraining force action on the body before the body comes to rest.

When an incompressible fluid flows steadily, the sum of pressure energy, kinetic energy and potential energy per unit volume of the fluid remains constant. This is Bernoulli's theorem.

It relates the pressure difference between two points to change the potential energy and kinetic energy in the pipe.

Consider the velocity at the hole be $v$.

Applying the Bernoulli’s theorem on the top most layer and the hole

$ \Rightarrow {P_{atm}} + \rho gH + \dfrac{1}{2}\rho = {P_{atm}} + \rho gh + \dfrac{1}{2}\rho {V^2}$

Where ${P_{atm}}$is the pressure, $g$is the acceleration due to gravity,$\rho $is the density,

$\Rightarrow V = \sqrt {2g\left( {H - h} \right)} $

Time taken to reach the ground $t = \sqrt {\dfrac{{2h}}{g}} $

Then the horizontal range, $R = V \times t$

$ \Rightarrow \sqrt {2gH - 2gh} \times \sqrt {\dfrac{{2h}}{g}} $

Differentiating the range and equating it to zero gives the maximum horizontal range then we can say that

$\Rightarrow h = \dfrac{H}{2}$

**Hence option C is the correct option.**

**Note:**Potential energy is the stored energy inside the body, when the body is deformed.

When the body retains its original state, the potential energy stored in the body will get converted to kinetic energy.

Potential energy is the energy stored due to its location or configuration. The energy possessed by a body due its motion is termed as Kinetic energy.

Recently Updated Pages

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Which of the following amino acids is an essential class 12 chemistry JEE_Main

Which of the following is least basic A B C D class 12 chemistry JEE_Main

Out of the following hybrid orbitals the one which class 12 chemistry JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Vant Hoff factor when benzoic acid is dissolved in class 12 chemistry JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main