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Small identical bodies at a separation equal to radius of earth are situated in such a way that one of them is at the Earth surface and other 1 above the Earth surface the centre of gravity is at a height

Small identical bodies at a separation equal to radius of earth are situated in such a way that one of them is at the Earth surface and other 1 above the Earth surface the centre of gravity is at a height

Grade:12th pass

2 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
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Eshan
askIITians Faculty 2095 Points
5 years ago
To find the center of gravity, we first need to find out the gravitational force acting on the bodies.
On the body on the surface of earth, the force is
W_1=\dfrac{GMm}{R^2}

On the body at distance2Rfrom center of earth, the acting force is
W_2=\dfrac{GMm}{(2R)^2}

So the distance of center of gravity from the center of earth is
\dfrac{W_1(R)+W_2(2R)}{W_1+W_2}=\dfrac{6R}{5}

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