The energy required to take a satellite

Asked by admin @ 24/08/2021 in Physics viewed by 280 People

✪ Physics ✪

The energy required to take a satellite to a height 'h' above earth surface (radius of earth = 6.4 × 10³ km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal is :- a) 1.28 × 10⁴ kmb) 6.4 × 10³ kmc) 3.2 × 10³ kmd) 1.6 × 10³ km

Answered by admin @ 24/08/2021

★Given :

The energy required to take a satellite to a height 'h' above earth surface is E₁.
Kinetic energy required for the satellite to be in a circular orbit at this height is E₂ .
Radius of earth = 6.4 × 10³ km

★To find :

The value of h for which E₁ and E₂ are equal

★Solution :

Applying conservation of total energy,

(K.E + P.E)₁ = (K.E + P.E)₂ __(1)

K.E of satellite is zero at the earth's surface.

And if we define the potential energy to be zero at r = infinity,U = -GmM/r.

Therefore,

$\displaystyle \implies \sf E_1+\bigg(\frac{-GMm}{R} \bigg)= 0+\bigg(\frac{-GMm}{(R+h)} \bigg) \\$

$\displaystyle \implies \sf E_1 = \frac{GMm}{R} - \frac{GMm}{(R+h)} \\$

$\displaystyle \implies \sf E_1 = \frac{GMm(R+h)-GMm(R)}{R(R+h)} \\$

$\displaystyle \implies \sf E_1 = \frac{GMm(\cancel{R}+h-\cancel{R})}{R(R+h)} \\$

$\displaystyle \implies \sf E_1 = \frac{GMmh}{R(R+h)} \\$

We know :

$\mapsto \boxed{\sf V =\sqrt{\frac{GM}{r}}}\\$

$\therefore \sf V = \dfrac{GM}{R+h} \\$

Now,

Using the formula :

$\leadsto \boxed{\sf K.E = \frac{1}{2} mv^2 }\\$

$\implies \sf E_2 = \dfrac{1}{2} mv^2 \\$

$\implies \sf E_2 = \dfrac{1}{2} \times m\times \bigg(\sqrt{\dfrac{GM}{(R+h)}} \bigg) ^2 \\$

$\implies \sf E_2 = \dfrac{1}{2} \times m \times \dfrac{GM}{R+h} \\$

We have to find the value of h for which E₁ & E₂ are equal.Therefore,

$\implies \sf E_1 = E_2 \\$

$\displaystyle \implies \sf \frac{\cancel{GMm}h}{R\cancel{(R+h)}} = \frac{1}{2} \cancel{m}\bigg(\frac{\cancel{GM}}{\cancel{R+h}} \bigg)\\$

$\implies \sf \dfrac{h}{R} = \dfrac{1}{2} \\$

$\implies \sf 2h = R\\\\ \implies \sf h = \dfrac{R}{2} \\$

Given that R = 6.4 × 10³ km.

Substituting this value in the above equation,

$\implies \sf h = \dfrac{6.4 \times 10^3 }{2} \\$

$\implies \underline{\boxed{\bold{h = 3.2\times 10^3km}}}\\$

Therefore,

Option(C) is correct.

_____________

Two changes of state that require energy to be used

Asked by admin @ 22/11/2021 in Chemistry viewed by 313 persons

A fog over a lake. what two changes of state must occur to produce the fog? do the water molecules absorb or release energy during these changes of state? what …

What is the element required for solar energy conversion

Asked by admin @ 23/08/2021 in Science viewed by 316 persons

The element required for Solar energy conversion: A. Beryllium B. Silicon C. Tantalum D. Ultra pure carbon

How many satellites are required to cover the earth

Asked by admin @ 20/08/2021 in Computer Science viewed by 275 persons

How many satellites are required to cover the earth?

What is the potential energy of the satellite earth system

Asked by admin @ 05/11/2021 in Physics viewed by 272 persons

A satellite in earth orbit has a mass of 99 kg and is at an altitude of 2.02 106 m. (assume that u = 0 as r â â.) (a) …

The energy required to remove an electron from an atom

Asked by admin @ 27/09/2021 in Chemistry viewed by 324 persons

What is the energy required to remove an electron from an atom in the gaseous state called

The process requiring the absorption of energy is

Asked by admin @ 25/08/2021 in Chemistry viewed by 298 persons

The process requiring the absorption of energy...a)F gives F^- b)Cl gives Cl^- c)O gives O^2- d) H gives H ^-

Energy required for atp synthesis in ps2 comes from

Asked by admin @ 11/08/2021 in Biology viewed by 291 persons

Energy required for atp synthesis in ps2 comes from

The energy required to start a chemical reaction is called

Asked by admin @ 02/08/2021 in Chemistry viewed by 335 persons

Energy required to start a chemical reaction is called

Does passive transport require energy

Asked by maham237 @ 11/01/2021 in Chemistry viewed by 246 persons

Why does passive transport not require the cell to use energy to move molecules across themembrane? The molecules use protein pumps to move molecules across the membrane The molecules are …

Why doesn t passive transport require energy

Asked by maham237 @ 06/01/2021 in Chemistry viewed by 261 persons

Why does passive transport not require the cell to use energy to move molecules across the membrane? The molecules use protein pumps to move molecules across the membrane The molecules …

What is the term for reactions that require energy input

Asked by admin @ 07/11/2021 in Chemistry viewed by 326 persons

A(n) ________ chemical reaction releases energy, whereas a(n) ________ reaction requires an input of energy.

Should students be required to take spanish classes persuasive essay

Asked by admin @ 29/10/2021 in English viewed by 333 persons

Question 10 of 25Foreign languages are extremely important to students' education. After taking my first Spanish course, I saw a significant increase in my English grade. As a student in …

Energy required for the ionisation of 0.02 gram atom

Asked by admin @ 20/08/2021 in Chemistry viewed by 275 persons

Energy required for ionisation of 0.02 gm atom of magnesium is xKJ . The amount of energy required to ionize 1 atom of magnesium is

An energy of 24.6 ev is required to remove

Asked by admin @ 13/08/2021 in Physics viewed by 251 persons

An energy of 24.6 eV is required to remove one of that electrons from a neutal helium atom. The enegy (in eV)required to remove both the electrons from a netural …