Question

solve this guys plz faster....
I will mark as brainlist answer...​

Answer 1

Question :

A satellite is projected vertically upwards from an Earth station . At what height above the earth's surface will the force on the satellite due to Earth will be reduced to half of the value of the earth station ?

Radius of Earth is 6400 km .

Solution :

Let the force be F originally .

Then the final force is reduced to half , which is F/2 .

We know that the formula for the force acting on the object is :

$F=\dfrac{GMm}{r^2}$

M is the mass of the Earth .

m is the mass of the object .

r is the radius of the Earth .

Let the height of the satellite be h .

Then R = r + h where r is the radius of Earth .

According to the question :

$\dfrac{F}{2}=\dfrac{GMm}{(r+h)^2}\\\\\implies \dfrac{GMm}{2r^2}=\dfrac{GMm}{(r+h)^2}\\\\\implies (r+h)^2=2r^2\\\\\implies r^2+h^2+2rh=2r^2\\\\\implies h^2+2rh-r^2=0\\\\\text{By using quadratic formula and taking only positive value we have :}\\\\\implies h=\dfrac{-2r\pm \sqrt{4r^2+4r^2}}{2}\\\\\implies h=\dfrac{-2r\pm \sqrt{8r^2}}{2}\\\\\implies h=\dfrac{-2r+2\sqrt{2}r}{2}\\\\\implies h=r(\sqrt{2}-1)\\\\\implies h=6400km\times 0.414\\\\\implies h =2649.6km$

The height will be 2649.6 km .

Answer 2

Answer:

Hey mate.....

The height will be 2649.6 m

Hope it helps!!! ✌